Q3 of 186 Page 332

Prove each of the following identities:

Consider the left – hand side:

L.H.S. =

= (1/sec²θ) + (1/cosec² θ) (∵ 1 + tan² θ = sec² θ and 1 + tan² θ = sec² θ)

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

= 1

= R.H.S.

Hence, proved.

Prove each of the following identities:

(1 – cos² θ) sec² θ = tan² θ

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