How do you simplify #(2sinxcos^3x-2sin^3xcosx)#?

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Answer 1 · 2016-10-11T00:31:51

Factor out the GCF:

#=2sinxcosx(cos^2x - sin^2x)#

#=2sinxcosx(1 - sin^2x - sin^2x)#

#=2sinxcosx(1 - 2sin^2x)#

Apply the identities #sin2x = 2sinxcosx# and #cos2x = 1 - 2sin^2x#.

#=sin2xcos2x#

Hopefully this helps!