Question #85875

1 Answer
ProfLayton
Aug 4, 2017

(sin3x+cos3x)(cosx-sinx)

Explanation:

sin2x+cos4x=sin(3x-x)+cos(3x+x)
=sin3xcosx-cos3xsinx+cos3xcosx-sin3xsinx
=sin3xcosx-sin3xsinx+cos3xcosx-cos3xsinx
=sin3x(cosx-sinx)+cos3x(cosx-sinx)
=(sin3x+cos3x)(cosx-sinx)

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