如何用泰勒公式证明sin（x-y)=sinxcosy-cosxsiny 证明cos(x+y)=cosxcosy-sinxsiny？
\u8bc1\u660esin(x+y)=sinx*cosy+cosx*siny\u7684\u8fc7\u7a0b\u63a8\u8350\u4e00\u79cd\u5411\u91cf\u6cd5\u8bc1\u660e\uff1a
\u5728\u5355\u4f4d\u5706\u4e0a\u53d6\u4e24\u70b9M N\uff0c\u4e0ex\u8f74\u7684\u5939\u89d2\u5206\u522b\u662fx,pi/2+y
\u5219M\uff08cosx,sinx\uff09,N(-siny,cosy)
\uff08OM\uff0cON\uff09=
cos(OM,ON)=cos(pi/2+y-x)=sin(x-y)=OM\u70b9\u4e58ON/(|OM||ON|)
\u5373 sin(x-y)=sinxcosy-cosxsiny
\u7528-y\u66ff\u6362y\u53ef\u5f97\uff1asin(x+y)=sinxcosy+cosxsiny
\u8bc1\u6bd5
\u7c7b\u4f3c\u7684\u53ef\u5f97\u5230cos(x+y)\u7684\u516c\u5f0f
\u600e\u4e48\u8bc1\u660e\u4e24\u89d2\u548c\u7684\u4f59\u5f26\u516c\u5f0fCos(x+y)=CosxCosy-SinxSiny
\u60ac\u8d4f\u5206\uff1a0 - \u89e3\u51b3\u65f6\u95f4\uff1a2010-6-13 19:25
\u63d0\u95ee\u8005\uff1a 244169321 - \u4e09\u7ea7\u6700\u4f73\u7b54\u6848\u7b2c\u4e00\u4e2a\u516c\u5f0f\u7684\u8bc1\u660e:
\u53f3\u8fb9=2*sin[(A+B)/2]*cos[(A-B)/2]
=2*[sin(A/2)*cos(B/2)+cos(A/2)sin(B/2)]*[cos(A/2)cos(B/2)+sin(A/2)sin(B/2)]
=2*sin(A/2)*cos(A/2)*cos(B/2)*cos(B/2)+2*cos(A/2)*cos(A/2)*sin(B/2)*cos(B/2)+2*sin(A/2)*sin(A/2)*cos(B/2)*sin(B/2)+2*sin(A/2)*cos(A/2)*sin(B/2)*sin(B/2)
=sinA*[cos(B/2)*cos(B/2)+sin(B/2)*sin(B/2)]+sin(B/2)*[cos(B/2)*cos(B/2)+sin(B/2)*sin(B/2)]
=sinA+sinB=\u5de6\u8fb9
\u8bc1\u6bd5
\u5176\u4e2d\u7528\u5230\u516c\u5f0f:
sinA=2*sin(A/2)*cos(A/2),sinB=2*cos(B/2)*sin(B/2)
cos(B/2)*cos(B/2)+sin(B/2)*sin(B/2)=1
\u5176\u4ed6\u7684\u516c\u5f0f\u4f9d\u6b64\u7c7b\u63a8,\u81ea\u5df1\u63a8\u63a8\u770b\u5427!
\u53c2\u8003\u8d44\u6599\uff1ahttp://zhidao.baidu.com/question/34994365.html?si=1
\u8bbex,y\u4e3a\u4efb\u610f\u89d2\uff0c\u6c42\u8bc1\uff1acos(x+y)=cosxcosy\u2014sinxsiny
\u60ac\u8d4f\u5206\uff1a20 - \u89e3\u51b3\u65f6\u95f4\uff1a2008-8-15 13:30
\u8fc7\u7a0b\u8be6\u7ec6\u4e9b\u554a~~~
\u8c22\u8c22\u5566~~~
\u63d0\u95ee\u8005\uff1a \u65e0\u6cd5\u65e0\u5929131 - \u4e00\u7ea7\u6700\u4f73\u7b54\u6848\u8fd9\u4e2a\u8981\u7528\u5fae\u79ef\u5206\u6765\u8bc1\u660e\u7684 \u529d\u4f60\u522b\u4e0b\u60f3\u4e86
\u6700\u7b80\u5355\u7684\u5c31\u662f\u5750\u6807\u8f74\u7684\u53d8\u6362\u00b7\u00b7\u00b7\u8bfe\u672c\u4e0a\u5c31\u6709\uff0c\u8ba4\u771f\u770b\u8bfe\u672c\u53bb
\u521a\u9ad8\u8003\u5b8c\uff0c\u73b0\u5728\u5c31\u5565\u90fd\u4e0d\u4f1a\u4e86\uff0c\u4eba\u554a\uff01\u5509\uff01\u7ed9\u4f60\u5728\u7f51\u4e0a\u627e\u7684
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