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Verify the identity cos^3xsin^2x = (sin^2x-sin^4x)cosx

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2 Answers

cosx^3sinx^2 = cosx(cosx^2)(1-cosx^2) = cosx(1-sinx^2)(1- (1-sinx^2)) = cosx(1-sinx^2)(sinx^2)
 
=cosx(sinx^2-sinx^4)
 
 
 
Cos 3 X  . Sin 2 X =                   ( Sin2 X - Sin 4 X ) COSX
 
 COS2 X . Sin2X . CosX =
 
  ( 1 _ Sin2 X ) Sin2 X . COSX
 
(  SIN2 X - SIN4 X ) . COSX   =   ( Sin2 X - Sin4 X ) COS X