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!

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