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.


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