Q2 of 186 Page 332

Prove each of the following identities:

(1 – cos2 θ) sec2 θ = tan2 θ

Consider the left – hand side:

L.H.S. = (1 – cos2 θ) sec2 θ


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


= (sin2θ) × (cos2θ)


= tan2 θ


= R.H.S.


Hence, proved.


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