Show that (1-cosx)^1/2*(1+cosx)^1/2=sinx

(1-cosx)^1/2*(1+cosx)^1/2=sinx

=sqrt(1-cosx)*sqrt(1+cosx)

=sqrt(1-cos^2x)

=sinx

Is it acceptable? Thank You.

You got it. All I would do differently is show that 1 - cos(x)^2 is sin(x)^2

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

But that's just a minor issue. You seem to understand what you're doing.

To Prove:-
(1- cosx)^1/2 * (1+ cosx)^1/2 = sinx
Left Hand Side :

(1- cosx)^1/2 * (1+ cosx)^1/2

= [ (1- cosx)* (1+ cosx)]^1/2

= [ 1 - cos^2x]^ 1/2, But [ (a- b )(a + b)] = a^2 - b^2

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

= [sinx]^2*1/2,

= sinx = Right Hand Side

Hence Proved.