Prove? sin2x-4cosxsin^3x = sin2xcos2x

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Answer 1 · 2018-03-21T05:19:32

Please refer to a Proof in the Explanation.

$sin2x-4cosxsin^3x$ ,

$=sin2x-(2sinxcosx)(2sin^2x)$ ,

$=sin2x-(sin2x)(2sin^2x)$ ,

$=(sin2x)(1-2sin^2x)$ ,

$rArr sin2x-4cosxsin^3x=sin2xcos2x$ .

BONUS :

Since, $sin2xcos2x=1/2*2sin2xcos2x$ ,

$:. sin2x-4cosxsin^3x=sin2xcos2x=1/2sin4x$ .