化简2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-cos2(x)cos^2(φ)
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化简2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-cos2(x)cos^2(φ)
据:cos2(x)=cosx^2-sinx^2=2cosx^2-1得:
2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-cos2(x)cos^2(φ)
=2sin^2(x)sin^2(φ)+cos^2(φ)
=(2sin^2(x)-1)*sin^2(φ)+sin^2(φ)+cos^2(φ)
=(sin^2(x)-cos^2(x))*sin^2(φ)+1
=-cos2(x)*(1-cos2φ)/2+1
2sin^2(x)sin^2(φ)+2cos^2(x)cos^2(φ)-cos2(x)cos^2(φ)
=2sin^2(x)sin^2(φ)+cos^2(φ)
=(2sin^2(x)-1)*sin^2(φ)+sin^2(φ)+cos^2(φ)
=(sin^2(x)-cos^2(x))*sin^2(φ)+1
=-cos2(x)*(1-cos2φ)/2+1
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