Prove the following identities.

Consider LHS,

LHS = +

We know that tan (90° - θ) = cotθ.

⇒ + = +

=

We know that (a + b)² = a² + 2ab + b².

⇒ + =

We know that cot²θ + 1 = cosec²θ.

⇒ + =

=

=

=

We know that = cosecθ and = cotθ.

⇒ + =

=

We know that = secθ.

⇒ + = 2secθ = RHS

Hence proved.