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).**