Q4 of 186 Page 332

Prove each of the following identities:
(1 + cos θ )(1 – cos θ)(1 + cot² θ) = 1

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.

Prove each of the following identities:

(cosec θ)(1 + cos θ)(cosec θ – cot θ) = 1

Prove each of the following identities:

Prove each of the following identities:(1 + cos θ )(1 – cos θ)(1 + cot2 θ) = 1