化简sin^2Xsin^2Y+cos^2Xcos^2Y-0.5cos2Xcos2Y
问题描述：
化简sin^2Xsin^2Y+cos^2Xcos^2Y-0.5cos2Xcos2Y
答
(sinx)^2(siny)^2+(cosx)^2(cosy)^2-1/2*cos2xcos2y
=(1-cos2x)/2*(1-cos2y)/2+(1+cos2x)/2*(1+cos2y)/2-1/2*cos2xcos2y
=(1-cos2x-cos2y+cos2xcos2y)/4+(1+cos2x+cos2y+cos2xcos2y)/4-1/2*cos2xcos2y
=(1+cos2xcos2y)/2-1/2*cos2xcos2y
=1/22sinX-cosX=1求sinX+conX+1/sinX-cosX+1两端平方 4(sinx)^2-4sinxcosx+(cosx)^2=(sinx)^2+(cosx)^23(sinx)^2=4sinxcosx1)sinx=0，则cosx=-1，代入得 02)sinx不为0，则 3sinx=4cosx，sinx=4/3*cosx，代入已知等式得 cosx=3/5，sinx=4/5代入得 20或2