Prove the following identities.

Consider LHS,

LHS = +

We know that sin (90° - θ) = cosθ and cos (90° - θ) = sinθ.

⇒ + = +

Taking LCM,

⇒ + =

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

⇒ + =

We know that 1 –sin²θ = cos²θ.

⇒ + =

= 2 ()

We know that = secθ.

∴ + = 2secθ = RHS

Hence proved.