Answer :

Consider LHS,

LHS = +

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

⇒ + = +

Taking LCM,

⇒ + =

We know that (a + b) (a – b) = a^{2} – b^{2}.

⇒ + =

We know that 1 –sin^{2}θ = cos^{2}θ.

⇒ + =

= 2 ()

We know that = secθ.

∴ + = 2secθ = RHS

Hence proved.

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