Q3 of 186 Page 332

Prove each of the following identities:

Consider the left – hand side:

L.H.S. =

= (sin²θ) + (1/sec² θ) (∵ 1 + tan² θ = sec² θ)

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

= 1

= R.H.S.

Hence, proved.

Prove each of the following identities:

(sec² θ – 1)(cosec² θ – 1) = 1

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