Prove each of the following identities:

Consider the left – hand side:

L.H.S. = cos2 θ +


= cos2 θ + (∵ 1 + cot2 θ = cosec2 θ)


= cos2 θ + sin2 θ


= ( – cos2 θ) × cos2 θ (∵ sin2θ + cos2 θ = 1)


= – 1


= R.H.S.


Hence, proved.


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