Prove 1 + ( 1 / tan²(x) ) = ( 1 / sin²(x) ). Is this an identity?

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

We
will use trigonometric identities to simplify.

We know that tanx =
sinx/cosx

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

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

Now we will
rewrite sin^2 x/sin^2 x = 1

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

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

= 1/sin^2
x..........q.e.d

==> Then the identity is
true.