Prove the trigonometric identity: (cot x)^2+1= (cosec x)^2.

We'll manage the right side, knowing that the cosecant
function is given by the ratio:

`cosec x = 1/(sin
x)`

We'll raise to square both
sides:

`cosec^2 x = 1/(sin^2
x)`

We'll re-write the
expression:

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

We'll multiply both sides by `sin^2 x`
:

`sin^2 x*cot^2 x + sin^2 x =
1`

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

The expression will
become:

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

We'll simplify by `sin^2 x ` and we'll get the
Pythagorean identity:

`cos^2 x + sin^2 x =
1`

`` Since the given expression led to the
Pythagorean identity, that means that the expression represents an identity,
too.