How to prove that: `sin^2xcos^3x=(sin^2x-sin^4x)cosx`

Expert Answers
justaguide eNotes educator| Certified Educator

The identity `sin^2xcos^3x=(sin^2x-sin^4x)cosx` has to be proved.

Start with the left hand side

`sin^2xcos^3x`

= `sin^2x*cos^2x*cos x`

= `sin^2x*(1 - sin^2x)*cosx`

= `(sin^2x - sin^4x)*cos x`

This proves that `sin^2xcos^3x=(sin^2x-sin^4x)cosx`

oldnick | Student

`sin^2xcos^3x=sin^2x(1-sin^2x)cosx=(sin^2x-sin^4x)cosx`