오늘도 삽질중

시박바 속성 변경하기

촬스우리촬스 — Tue, 27 Feb 2007 10:27:45 GMT

아.... 무려 반나절이다

APPBARDATA appBarData;
appBarData.cbSize = sizeof(appBarData);
appBarData.hWnd = (HWND)FindWindow("Shell_TrayWnd",NULL);
//appBarData.lParam = ret | 1;

//disable
appBarData.lParam = 0;
SHAppBarMessage(0x0000000a,&appBarData);

예전에 ABM_SETSTATE flag가 없어졌다

안되는 줄 알았더니 define만 없앴나보다.. OTL

나름 대로 shell 관련 com interface도 몇개 알게 되고 그나마 얻은게 몇가지 있는 걸로 위안

컴퓨터공학과 대학원생의 하루

촬스우리촬스 — Mon, 22 Jan 2007 13:52:39 GMT

컴퓨터 공학과 공대 대학원생의 하루..

프로그래머에 관한 오해 몇가지..

촬스우리촬스 — Fri, 12 Jan 2007 04:21:05 GMT

프로그래머에 관한 오해 몇가지..

xdebug, xlocale 관련 error

촬스우리촬스 — Thu, 11 Jan 2007 08:26:53 GMT

------ Build started: Project: unittest, Configuration: Debug Win32 ------
Compiling...
unittestDlg.cpp
c:\program files\microsoft visual studio 8\vc\include\xdebug(32) : warning C4229: anachronism used : modifiers on data are ignored
c:\program files\microsoft visual studio 8\vc\include\xdebug(32) : error C2365: 'operator new' : redefinition; previous definition was 'function'
c:\program files\microsoft visual studio 8\vc\include\xdebug(32) : error C2491: 'new' : definition of dllimport data not allowed
c:\program files\microsoft visual studio 8\vc\include\xdebug(32) : error C2078: too many initializers
c:\program files\microsoft visual studio 8\vc\include\xdebug(32) : error C2440: 'initializing' : cannot convert from 'int' to 'void *'
        Conversion from integral type to pointer type requires reinterpret_cast, C-style cast or function-style cast
c:\program files\microsoft visual studio 8\vc\include\xdebug(32) : error C2143: syntax error : missing ';' before '('
c:\program files\microsoft visual studio 8\vc\include\xdebug(32) : error C2226: syntax error : unexpected type 'size_t'
c:\program files\microsoft visual studio 8\vc\include\xdebug(33) : error C2059: syntax error : ')'
c:\program files\microsoft visual studio 8\vc\include\xdebug(36) : warning C4229: anachronism used : modifiers on data are ignored
c:\program files\microsoft visual studio 8\vc\include\xdebug(36) : error C2365: 'operator new' : redefinition; previous definition was 'function'
c:\program files\microsoft visual studio 8\vc\include\xdebug(36) : error C2491: 'new' : definition of dllimport data not allowed
c:\program files\microsoft visual studio 8\vc\include\xdebug(36) : error C2078: too many initializers
c:\program files\microsoft visual studio 8\vc\include\xdebug(36) : error C2440: 'initializing' : cannot convert from 'int' to 'void *'
        Conversion from integral type to pointer type requires reinterpret_cast, C-style cast or function-style cast
c:\program files\microsoft visual studio 8\vc\include\xdebug(36) : error C2143: syntax error : missing ';' before '['
c:\program files\microsoft visual studio 8\vc\include\xdebug(36) : error C3409: empty attribute block is not allowed
c:\program files\microsoft visual studio 8\vc\include\xdebug(36) : error C2226: syntax error : unexpected type 'size_t'
c:\program files\microsoft visual studio 8\vc\include\xlocale(138) : error C2059: syntax error : 'string'
c:\program files\microsoft visual studio 8\vc\include\xlocale(139) : error C2091: function returns function
c:\program files\microsoft visual studio 8\vc\include\xlocale(139) : error C2802: static member 'operator new' has no formal parameters
c:\program files\microsoft visual studio 8\vc\include\xlocale(139) : error C2333: 'std::locale::facet::operator new' : error in function declaration; skipping function body
c:\program files\microsoft visual studio 8\vc\include\xlocale(144) : error C2059: syntax error : 'string'
c:\program files\microsoft visual studio 8\vc\include\xlocale(146) : error C2091: function returns function
c:\program files\microsoft visual studio 8\vc\include\xlocale(146) : error C2556: 'void *(__cdecl *std::locale::facet::operator new(void))(size_t,const std::_DebugHeapTag_t &,char *,int)' : overloaded function differs only by return type from 'void *(__cdecl *std::locale::facet::operator new(void))(size_t)'
        c:\program files\microsoft visual studio 8\vc\include\xlocale(138) : see declaration of 'std::locale::facet::operator new'
c:\program files\microsoft visual studio 8\vc\include\xlocale(147) : error C2059: syntax error : 'return'
c:\program files\microsoft visual studio 8\vc\include\xlocale(147) : error C2238: unexpected token(s) preceding ';'
c:\program files\microsoft visual studio 8\vc\include\xlocale(150) : error C2628: 'std::locale::facet' followed by 'void' is illegal (did you forget a ';'?)
c:\program files\microsoft visual studio 8\vc\include\xlocale(152) : error C2817: return type for 'operator delete' must be 'void'
c:\program files\microsoft visual studio 8\vc\include\xlocale(152) : error C2333: 'std::locale::operator delete' : error in function declaration; skipping function body
c:\program files\microsoft visual studio 8\vc\include\xlocale(164) : error C2523: 'std::locale::~facet' : destructor tag mismatch
c:\program files\microsoft visual studio 8\vc\include\xlocale(169) : error C2146: syntax error : missing ')' before identifier '_Initrefs'
c:\program files\microsoft visual studio 8\vc\include\xlocale(169) : error C2146: syntax error : missing ';' before identifier '_Initrefs'
c:\program files\microsoft visual studio 8\vc\include\xlocale(169) : error C2071: 'std::locale::size_t' : illegal storage class
c:\program files\microsoft visual studio 8\vc\include\xlocale(169) : error C2059: syntax error : ')'
c:\program files\microsoft visual studio 8\vc\include\xlocale(169) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(169) : error C2864: 'std::locale::_Initrefs' : only static const integral data members can be initialized within a class
c:\program files\microsoft visual studio 8\vc\include\xlocale(169) : error C2143: syntax error : missing ';' before ':'
c:\program files\microsoft visual studio 8\vc\include\xlocale(170) : error C2065: '_Initrefs' : undeclared identifier
c:\program files\microsoft visual studio 8\vc\include\xlocale(170) : error C3861: '_Refs': identifier not found
c:\program files\microsoft visual studio 8\vc\include\xlocale(171) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(171) : error C2473: '' : looks like a function definition, but there is no parameter list.
c:\program files\microsoft visual studio 8\vc\include\xlocale(174) : error C2059: syntax error : 'private'
c:\program files\microsoft visual studio 8\vc\include\xlocale(174) : error C2143: syntax error : missing ';' before ':'
c:\program files\microsoft visual studio 8\vc\include\xlocale(71) : error C2059: syntax error : ':'
c:\program files\microsoft visual studio 8\vc\include\xlocale(112) : error C2327: 'std::locale::size_t' : is not a type name, static, or enumerator
c:\program files\microsoft visual studio 8\vc\include\xlocale(118) : error C2327: 'std::locale::size_t' : is not a type name, static, or enumerator
c:\program files\microsoft visual studio 8\vc\include\xlocale(126) : error C2327: 'std::locale::size_t' : is not a type name, static, or enumerator
c:\program files\microsoft visual studio 8\vc\include\xlocale(134) : error C3861: 'facet_Register': identifier not found
c:\program files\microsoft visual studio 8\vc\include\xlocale(175) : error C2065: 'facet' : undeclared identifier
c:\program files\microsoft visual studio 8\vc\include\xlocale(175) : error C2059: syntax error : ')'
c:\program files\microsoft visual studio 8\vc\include\xlocale(177) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(177) : error C2143: syntax error : missing ',' before '&'
c:\program files\microsoft visual studio 8\vc\include\xlocale(177) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(178) : error C2143: syntax error : missing ';' before '&'
c:\program files\microsoft visual studio 8\vc\include\xlocale(178) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(178) : error C2365: 'std::facet' : redefinition; previous definition was 'function'
        c:\program files\microsoft visual studio 8\vc\include\xlocale(177) : see declaration of 'std::facet'
c:\program files\microsoft visual studio 8\vc\include\xlocale(178) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(178) : error C2143: syntax error : missing ',' before '&'
c:\program files\microsoft visual studio 8\vc\include\xlocale(178) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(178) : error C2801: 'std::operator =' must be a non-static member
c:\program files\microsoft visual studio 8\vc\include\xlocale(186) : error C2516: 'facet' : is not a legal base class
c:\program files\microsoft visual studio 8\vc\include\xlocale(196) : error C2061: syntax error : identifier 'facet'
c:\program files\microsoft visual studio 8\vc\include\xlocale(211) : error C2061: syntax error : identifier 'facet'
c:\program files\microsoft visual studio 8\vc\include\xlocale(216) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(216) : error C2143: syntax error : missing ',' before '&'
c:\program files\microsoft visual studio 8\vc\include\xlocale(219) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(219) : error C2143: syntax error : missing ',' before '&'
c:\program files\microsoft visual studio 8\vc\include\xlocale(223) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(223) : error C2143: syntax error : missing ',' before '&'
c:\program files\microsoft visual studio 8\vc\include\xlocale(227) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(227) : error C2143: syntax error : missing ',' before '&'
c:\program files\microsoft visual studio 8\vc\include\xlocale(230) : error C2143: syntax error : missing ';' before '*'
c:\program files\microsoft visual studio 8\vc\include\xlocale(230) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(230) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(232) : error C2146: syntax error : missing ';' before identifier '_Catmask'
c:\program files\microsoft visual studio 8\vc\include\xlocale(232) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(232) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(234) : error C2146: syntax error : missing ';' before identifier '_Name'
c:\program files\microsoft visual studio 8\vc\include\xlocale(234) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(234) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(199) : error C2027: use of undefined type 'locale'
        c:\program files\microsoft visual studio 8\vc\include\xlocale(197) : see declaration of 'locale'
c:\program files\microsoft visual studio 8\vc\include\xlocale(201) : error C2065: 'none' : undeclared identifier
c:\program files\microsoft visual studio 8\vc\include\xlocale(202) : error C2614: '_Locimp' : illegal member initialization: '_Name' is not a base or member
c:\program files\microsoft visual studio 8\vc\include\xlocale(202) : error C2614: '_Locimp' : illegal member initialization: '_Catmask' is not a base or member
c:\program files\microsoft visual studio 8\vc\include\xlocale(202) : error C2614: '_Locimp' : illegal member initialization: '_Facetvec' is not a base or member
c:\program files\microsoft visual studio 8\vc\include\xlocale(202) : error C2614: '_Locimp' : illegal member initialization: 'facet' is not a base or member
c:\program files\microsoft visual studio 8\vc\include\xlocale(204) : error C2027: use of undefined type 'locale'
        c:\program files\microsoft visual studio 8\vc\include\xlocale(197) : see declaration of 'locale'
c:\program files\microsoft visual studio 8\vc\include\xlocale(206) : error C2039: '_Catmask' : is not a member of '_Locimp'
        c:\program files\microsoft visual studio 8\vc\include\xlocale(185) : see declaration of '_Locimp'
c:\program files\microsoft visual studio 8\vc\include\xlocale(206) : error C2039: '_Name' : is not a member of '_Locimp'
        c:\program files\microsoft visual studio 8\vc\include\xlocale(185) : see declaration of '_Locimp'
c:\program files\microsoft visual studio 8\vc\include\xlocale(207) : error C2614: '_Locimp' : illegal member initialization: '_Name' is not a base or member
c:\program files\microsoft visual studio 8\vc\include\xlocale(207) : error C2614: '_Locimp' : illegal member initialization: '_Catmask' is not a base or member
c:\program files\microsoft visual studio 8\vc\include\xlocale(207) : error C2614: '_Locimp' : illegal member initialization: '_Facetvec' is not a base or member
c:\program files\microsoft visual studio 8\vc\include\xlocale(207) : error C2614: '_Locimp' : illegal member initialization: 'facet' is not a base or member
c:\program files\microsoft visual studio 8\vc\include\xlocale(213) : error C2065: '_Pfacet' : undeclared identifier
c:\program files\microsoft visual studio 8\vc\include\xlocale(213) : error C2065: '_Id' : undeclared identifier
c:\program files\microsoft visual studio 8\vc\include\xlocale(247) : error C2065: '_Fac' : undeclared identifier
c:\program files\microsoft visual studio 8\vc\include\xlocale(247) : error C2275: 'size_t' : illegal use of this type as an expression
        e:\my projects\unittest\unittest\stdafx.cpp : see declaration of 'size_t'
c:\program files\microsoft visual studio 8\vc\include\xlocale(247) : error C2146: syntax error : missing ')' before identifier '_Id'
c:\program files\microsoft visual studio 8\vc\include\xlocale(247) : error C2078: too many initializers
c:\program files\microsoft visual studio 8\vc\include\xlocale(247) : error C2275: 'size_t' : illegal use of this type as an expression
        e:\my projects\unittest\unittest\stdafx.cpp : see declaration of 'size_t'
c:\program files\microsoft visual studio 8\vc\include\xlocale(248) : error C2059: syntax error : ')'
c:\program files\microsoft visual studio 8\vc\include\xlocale(249) : error C2143: syntax error : missing ';' before '{'
c:\program files\microsoft visual studio 8\vc\include\xlocale(249) : error C2447: '{' : missing function header (old-style formal list?)
c:\program files\microsoft visual studio 8\vc\include\xlocale(265) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(265) : error C2143: syntax error : missing ',' before '<'
c:\program files\microsoft visual studio 8\vc\include\xlocale(273) : error C2270: '()' : modifiers not allowed on nonmember functions
c:\program files\microsoft visual studio 8\vc\include\xlocale(273) : error C2801: 'operator ()' must be a non-static member
c:\program files\microsoft visual studio 8\vc\include\xlocale(291) : error C2270: 'combine' : modifiers not allowed on nonmember functions
c:\program files\microsoft visual studio 8\vc\include\xlocale(294) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(294) : error C2904: 'locale' : name already used for a template in the current scope
        c:\program files\microsoft visual studio 8\vc\include\xlocale(197) : see declaration of 'locale'
c:\program files\microsoft visual studio 8\vc\include\xlocale(307) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(307) : error C3861: '_Init': identifier not found
c:\program files\microsoft visual studio 8\vc\include\xlocale(308) : error C2550: 'locale' : constructor initializer lists are only allowed on constructor definitions
c:\program files\microsoft visual studio 8\vc\include\xlocale(309) : error C2227: left of '->_Incref' must point to class/struct/union/generic type
        type is ''unknown-type''
c:\program files\microsoft visual studio 8\vc\include\xlocale(309) : error C3861: '_Getgloballocale': identifier not found
c:\program files\microsoft visual studio 8\vc\include\xlocale(310) : warning C4508: 'locale' : function should return a value; 'void' return type assumed
c:\program files\microsoft visual studio 8\vc\include\xlocale(312) : error C2065: '_Uninitialized' : undeclared identifier
c:\program files\microsoft visual studio 8\vc\include\xlocale(313) : error C2448: 'locale' : function-style initializer appears to be a function definition
c:\program files\microsoft visual studio 8\vc\include\xlocale(316) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(316) : error C2143: syntax error : missing ',' before '&'
c:\program files\microsoft visual studio 8\vc\include\xlocale(317) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(317) : error C2065: '_Right' : undeclared identifier
c:\program files\microsoft visual studio 8\vc\include\xlocale(317) : error C2228: left of '._Ptr' must have class/struct/union
        type is ''unknown-type''
c:\program files\microsoft visual studio 8\vc\include\xlocale(318) : error C2550: 'locale' : constructor initializer lists are only allowed on constructor definitions
c:\program files\microsoft visual studio 8\vc\include\xlocale(319) : error C2227: left of '->_Incref' must point to class/struct/union/generic type
        type is ''unknown-type''
c:\program files\microsoft visual studio 8\vc\include\xlocale(320) : warning C4508: 'locale' : function should return a value; 'void' return type assumed
c:\program files\microsoft visual studio 8\vc\include\xlocale(322) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(322) : error C2143: syntax error : missing ',' before '&'
c:\program files\microsoft visual studio 8\vc\include\xlocale(324) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
c:\program files\microsoft visual studio 8\vc\include\xlocale(324) : error C2084: function 'int locale(const int) throw()' already has a body
        c:\program files\microsoft visual studio 8\vc\include\xlocale(316) : see previous definition of 'locale'
c:\program files\microsoft visual studio 8\vc\include\xlocale(324) : fatal error C1003: error count exceeds 100; stopping compilation
Build log was saved at "file://e:\My Projects\unittest\unittest\Debug\BuildLog.htm"
unittest - 126 error(s), 4 warning(s)
========== Build: 0 succeeded, 1 failed, 0 up-to-date, 0 skipped ==========

이놈의 정체는...

새로 추가한 header를

#ifdef _DEBUG
#define new DEBUG_NEW
#endif

이놈 밑에 뒀다는거다... ㅡㅡ 헐..

fatal error RC1107

촬스우리촬스 — Thu, 11 Jan 2007 08:13:54 GMT

http://forums.microsoft.com/MSDN/ShowPost.aspx?PostID=123870&SiteID=1

include 파일 path에 ....\ 이게 들어가면 안돼는군... 아놔.. 버그야 뭐야..

CppUnit의 세계로

촬스우리촬스 — Thu, 11 Jan 2007 04:46:02 GMT

CppUnit의 세계로~

How to use cppunit

촬스우리촬스 — Thu, 11 Jan 2007 04:44:36 GMT

[펌]CppUnit

cppunit을 사용하기 위한 단계별 작업

촬스우리촬스 — Thu, 11 Jan 2007 04:27:13 GMT

CPPUnit 을 사용하기 위한 단계별 작업

UpdateAllViews

촬스우리촬스 — Mon, 04 Dec 2006 10:29:30 GMT

UpdateAllViews.

Document와 연결된 모든 View의 OnUpdate를 호출 한다.

----------------------------------------------------
오늘의 삽질
----------------------------------------------------
MDI Project를 만든후 CView를 상속받은 기본 view를 ScrollView로 바꾸기 위해
모두 바꾸기로 CView를 CScrollView로 변경.

OnUpdate 호출 안됌

3시간 삽질

ㅜㅜ

void CTestView::OnUpdate(CScrollView* pSender, LPARAM lHint, CObject* pHint);

이놈이 문제.

UpdateAllView호출시 ScrollView의 Onupdate로 바로 연결 되지 않음

void CTestView::OnUpdate(CView*.....) 로 변경 후 정상 동작

아뉘미...ㅇㅎ놰먀도해뱌멎ㄷ래ㅑㅓㅐ도
ㅈㄷㅂ햊댜ㅓ래쟈ㅓ랴

삼각함수 정리

촬스우리촬스 — Sat, 02 Dec 2006 05:23:40 GMT

삼각함수 공식정리

１）　tanθ＝sinθ÷cosθ

　　　　２）　cos２θ＋sin２θ＝１，　　　　１＋tan２θ＝１/cos２θ

　　　　３）　cos(－θ)＝cosθ， sin(－θ)＝－sinθ， tan(－θ)＝－tanθ

　　　　４）　cos(π/２－θ)＝sinθ， sin(π/２－θ)＝cosθ， tan(π/２－θ)＝tanθ

　　　　５）　cos(π/２＋θ)＝－sinθ， sin(π/２＋θ)＝cosθ， tan(π/２＋θ)＝－tanθ

　　　　６）　cos(π＋θ)＝－cosθ， sin(π＋θ)＝－sinθ， tan(π＋θ)＝tanθ

　　　　　　　cos(２ｎπ＋θ)＝cosθ，　 sin(２ｎπ＋θ)＝sinθ

　　　　　　　cos(π－θ)＝－cosθ， sin(π－θ)＝sinθ，　 tan(π－θ)＝－tanθ

　　　　７）　cos(α＋β)＝cosβcosα－sinβsinα

　　　　　　　cos(α－β)＝cosβcosα＋sinβsinα

　　　　　　　sin(α＋β)＝cosβsinα＋sinβcosα

　　　　　　　sin(α－β)＝cosβsinα－sinβcosα

　　　　　　　tan(α＋β)＝(tanα＋tanβ)÷(１－tanαtanβ)

　　　　　　　tan(α－β)＝(tanα－tanβ)÷(１＋tanαtanβ)

　　　　８）　cos(２α)＝cos２α－sin２α， sin(２α)＝２cosαsinα， tan(２α)＝２tanα÷(１－tan２α)

　　　　　　　cos２(α/２)＝(１＋cosα)/２，sin２(α/２)＝(１－cosα)/２，tan２(α/２)＝(１－cosα)/(１＋cosα)

　　　　９）　cos(３α)＝－３cos３α＋４cosα， sin(３α)＝３sinα－４sin３α

　　　　10）　２cosα×cosβ＝{cos(α＋β)＋cos(α－β)}

　　　　　　　２sinα×sinβ＝－{cos(α＋β)－cos(α－β)}

　　　　　　　２sinα×cosβ＝{sin(α＋β)＋sin(α－β)}

　　　　　　　２cosα×sinβ＝{sin(α＋β)－sin(α－β)}

　　　　11）　cosα＋cosβ＝２cos{(α＋β)/２}cos{(α－β)/２}

　　　　　　　cosα－cosβ＝－２sin{(α＋β)/２}sin{(α－β)/２}

　　　　　　　sinα＋sinβ＝２sin{(α＋β)/２}cos{(α－β)/２}

　　　　　　　sinα－sinβ＝２cos{(α＋β)/２}sin{(α－β)/２}

　　　　12）　ａcosθ－ｂsinθ＝(ａ２＋ｂ２)１/２cos(θ＋α)

　　　　　　　ａcosθ＋ｂsinθ＝(ａ２＋ｂ２)１/２sin(θ－α)

　　　　13）　tan(θ/２)＝ｔのとき，次式が成立する。

　　　　　　　cosθ＝(１－ｔ２)/(１＋ｔ２)、　sinθ＝２ｔ/(１＋ｔ２)、　tanθ＝２ｔ/(１－ｔ２)