Question

How do you verify the identity `sin^(1/2)xcosx-sin^(5/2)xcosx=cos^3xsqrtsinx`?

Answer 1

`LHS=sin^(1/2)xcosx-sin^(5/2)xcosx`

`=sin^(1/2)xcosx-sin^2xsin^(1/2)xcosx`

`=sin^(1/2)xcosx(1-sin^2x)`

`=sin^(1/2)xcosx(cos^2x)`

`=cos^3xsqrtsinx=RHS`

Verified