化简:y=cos^4 x+2 sinxcosx-sin^4 x

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化简:y=cos^4 x+2 sinxcosx-sin^4 x

化简:y=cos^4 x+2 sinxcosx-sin^4 x
化简:y=cos^4 x+2 sinxcosx-sin^4 x

化简:y=cos^4 x+2 sinxcosx-sin^4 x
=(cos^4 x-sin^4 x) +2 sinxcosx
=(cos^2 x+sin^2 x)*(cos^2 x-sin^2 x) +2 sinxcosx
=cos^2 x-sin^2 x +2 sinxcosx
=(cos x-sin x )^2

y=(cos^2x+sin^2x)(cos^2x-sin^2x)+sin2x
=cos^2x-sin^2x+sin2x
=cos2x+sin2x
=根号2(sinπ/4cos2x+conπ/4sin2x)
=根号2sin(2x+π/4)