证明cos(x+y)=cosxcosy-sinxsiny?RT,用有关sin和cos的公式来证...用角度和向量什么的就算了...

Question

证明cos(x+y)=cosxcosy-sinxsiny?
RT,用有关sin和cos的公式来证...用角度和向量什么的就算了...

Answer 1

怎么证明两角和的余弦公式Cos(x+y)=CosxCosy-SinxSiny
0 - 解决时间：2010-6-13 19:25
244169321 - 三级最佳答案第一个公式的证明:
右边=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=左边
证毕
其中用到公式:
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
其他的公式依此类推,自己推推看吧!
设x,y为任意角,求证：cos(x+y)=cosxcosy—sinxsiny
20 - 解决时间：2008-8-15 13:30
无法无天131 - 一级最佳答案这个要用微积分来证明的 劝你别下想了
最简单的就是坐标轴的变换···课本上就有,认真看课本去
刚高考完,现在就啥都不会了,人啊!唉!给你在网上找的