Verify sin^1/2xcosx- sin^5/2xcosx=cos^3x((sinx))?

Question

((sinx))= Square root of sinx

Answer 1

LHS=sin^1/2xcosx[1-sin^2x]
=sin^1/2xcosx*cos^2x
=cos^3xsin^1/2x
=RHS
henceproved

Answer 2

sin^(1/2) (x) cosx- sin^5/2xcosx=cos^3x((sinx)
[√sin x] * cos x - sin² x * [√sin x] * cos x = cos³x [√sin x]
[√sin x] (cos x - sin² x cos x) = cos³x [√sin x]
cos x - sin² x cos x = cos³x
cos x (1 - sin² x) = cos³x
cos x * cos² x = cos³x
cos³x = cos³x CHECK