Prove? sin2x-4cosxsin^3x = sin2xcos2x

1 Answer
Ratnaker Mehta
Mar 21, 2018

Please refer to a Proof in the Explanation.

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#.

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