Q5 of 186 Page 332

Prove each of the following identities:

Consider the left – hand side:

L.H.S. = cot² θ –

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

= – 1

= R.H.S.

Hence, proved.

Prove each of the following identities:

(1 + cos θ )(1 – cos θ)(1 + cot² θ) = 1

Prove each of the following identities:

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

Prove each of the following identities: