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

Question

This is for my trig class, and the directions say to verify the identity. Thanks so much.

Answer 1

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)

Answer 2

 

 

 

_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