Prove each of the following identities: (1 + cos θ )(1 – cos θ)(1 + cot 2 θ) = 1

Question

Philoid · Accepted Answer

Consider the left – hand side:

L.H.S. = (1 + cos θ)(1 – cos θ)(1 + cot² θ)

= (1 – cos² θ) × cosec² θ (∵ 1 + cot² θ = cosec² θ)

= (sin² θ) × cosec² θ (∵ sin²θ + cos² θ = 1)

= 1

= R.H.S.

Hence, proved.