Prove that sin(x)+sin(x)cot^2(x)=csc(x)

We'll factor sin x and we'll
get:

`sin x*(1 + cot^2 x) = csc
x`

From Pythagorean identity, we'll
get:

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

We'll re-write the
expression:

`sinx*(1/(sin^2 x)) = csc
x`

We'll simplify and we'll
get:

`1/sin x = csc
x`

Since the result represents a basic
identity, then the given expression represents an identity,
too.