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.