verify the identity?

### 3 Answers

sin^1/2x cos x – sin^5/2x cosx = sin^(1/2)x (cos x – sin^2 x cos x)

= sqrt(sin x) (cos x) (1 – sin^2 x) = sqrt(sin x)(cos x)(cos^2 x)

= cos^3 x * sqrt(sin x)

cos x (sin x)^1/2 – cos x (sin x)^(5/2)

= cos x sin(x)^1/2 [ 1 – sin^2(x) ]

= cos x sin(x)^1/2 [ cos^2(x) ]

= cos^3(x) √(sin x)

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

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

= cos^3xsin^1/2x