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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