化简sin^2Xsin^2Y+cos^2Xcos^2Y-0.5cos2Xcos2Y
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/28 22:38:50
化简sin^2Xsin^2Y+cos^2Xcos^2Y-0.5cos2Xcos2Y
(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
=1/2
再问: 2sinX-cosX=1求sinX+conX+1/sinX-cosX+1
再答: 两端平方 4(sinx)^2-4sinxcosx+(cosx)^2=(sinx)^2+(cosx)^2 3(sinx)^2=4sinxcosx 1)sinx=0,则cosx=-1,代入得 0 2)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 2 0或2
=(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
=1/2
再问: 2sinX-cosX=1求sinX+conX+1/sinX-cosX+1
再答: 两端平方 4(sinx)^2-4sinxcosx+(cosx)^2=(sinx)^2+(cosx)^2 3(sinx)^2=4sinxcosx 1)sinx=0,则cosx=-1,代入得 0 2)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 2 0或2
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