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Question
Prove that sec2θ − cos2θ = tan2θ + sin2θ
Solution
L.H.S = sec2θ − cos2θ
= 1 + tan2θ – cos2θ .......[∵ 1 + tan2θ = sec2θ]
= tan2θ + (1 – cos2θ)
= tan2θ + sin2θ ......`[(because sin^2theta +cos^2theta = 1),(therefore 1 - cos^2theta = sin^2theta)]`
= R.H.S
∴ sec2θ − cos2θ = tan2θ + sin2θ
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