Prove each of the following identities: (1 – cos 2 θ) sec 2 θ = tan 2 θ

Question

Philoid · Accepted Answer

Consider the left – hand side:

L.H.S. = (1 – cos² θ) sec² θ

= (sin²θ) × (1/cos²θ) (∵ sin² θ + cos² θ = 1)

= (sin²θ) × (cos²θ)

= tan² θ

= R.H.S.

Hence, proved.