Prove the identity cotx*sinx=cosx/(cos^2x+sin^2x)

We have to prove that cot x*sin x = cos x /((cos x)^2 +
(sin x)^2)

Now we know that (cos x)^2 + (sin x)^2 =
1

Also, cot x = cos x / sin
x

So cot x*sin x = (cos x / sin x)* sin x = cos
x

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

Therefore both the sides are equal to cos
x.

We prove that cot x*sin x = cos x /((cos
x)^2 + (sin x)^2).