化简2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-cos2(x)cos2(φ)
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化简2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-cos2(x)cos2(φ)化简2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-cos2(x)cos
化简2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-cos2(x)cos2(φ)
化简2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-cos2(x)cos2(φ)
化简2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-cos2(x)cos2(φ)
最后的乘积项用二倍角公式展开
原式=2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-[cos^2(x)-sin^2(x)][cos^2(φ)-sin^2(φ)]
=2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-[cos^2(x)cos^2(φ)-cos^2(x)sin^2(φ)-sin^2(x)cos^2(φ)+
sin^2(x)sin^2(φ)]
合并同类项 =sin^2(x)sin^2(φ)+cos^2(x)cos^2(φ)+cos^2(x)sin^2(φ)+sin^2(x)cos^2(φ)
=sin^2(x)[sin^2(φ)+cos^2(φ)]+cos^2(x)[cos^2(φ)+sin^2(φ)]
=sin^2(x)+cos^2(x)
=1
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