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Question
Prove that cot2θ – tan2θ = cosec2θ – sec2θ
Solution
L.H.S = cot2θ – tan2θ
= (cosec2θ − 1) − (sec2θ − 1) ......`[(because tan^2theta = sec^2theta - 1),(cot^2theta = "cosec"^2 theta - 1)]`
= cosec2θ − 1 − sec2θ + 1
= cosec2θ − sec2θ
= R.H.S
∴ cot2θ – tan2θ = cosec2θ – sec2θ
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