Prove each of the following identities:(1 + cot2 θ) sin2θ = 1

Consider the left – hand side:L.H.S. = (1 + cot2θ) × sin2 θ= (cosec2 θ) × sin2 θ (∵ 1 + cot2 θ = cosec2 θ)= 1= R.H.S.Hence, proved.

Q1 of 186 Page 332

Prove each of the following identities:
(1 + cot² θ) sin²θ = 1

Consider the left – hand side:

L.H.S. = (1 + cot²θ) × sin² θ

= (cosec² θ) × sin² θ (∵ 1 + cot² θ = cosec² θ)

= 1

= R.H.S.

Hence, proved.

Prove each of the following identities:

(1 – cos² θ)cosec² θ = 1

Prove each of the following identities:

(sec² θ – 1) cot² θ = 1

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