Prove that (sin x)^2*[1 + (cot x)^2] = 1

We know, as a consequence of Pythagorean identity,
that:

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

Let's see
how:

Pythagorean identity states
that:

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

We'll divide by (sin x)^2:

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

But (cos x)^2/ (sin
x)^2 = (cot x)^2

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

Now, we'll substitute what's inside brackets by the
equivalent above:

(sin x)^2*(1 + (cot x)^2) =
(sin x)^2*(1/(sin x)^2) = 1