求证：2sin^4 x+3/4sin^2 2x+5cos^4 x-cos3xcosx=2+2cos^2 x
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cos3x=cos(x+2x)=cosxcos2x-sinxsin2x=cosx(cos^2 x-sin^2 x)-2sin^2 xcosx=cos^3 x-3sin^2 xcosx
左边=2sin^4 x+3/4*4sin^2 xcos^2 x+5cos^4 x-cos^4 x+3sin^2 xcos^2 x
=2sin^4 x+4cos^4 x+6sin^2 xcos^2 x
=2(sin^2 x+cos^2 x)(sin^2 x+2cos^2 x)
=2(1+cos^2 x)
=右边
左边=2sin^4 x+3/4*4sin^2 xcos^2 x+5cos^4 x-cos^4 x+3sin^2 xcos^2 x
=2sin^4 x+4cos^4 x+6sin^2 xcos^2 x
=2(sin^2 x+cos^2 x)(sin^2 x+2cos^2 x)
=2(1+cos^2 x)
=右边
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