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Question
Prove the following:
(sinθ + cosecθ)2 + (cosθ + secθ)2 = tan2θ + cot2θ + 7
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Solution
L.H.S. = (sinθ + cosecθ)2 + (cosθ + secθ)2
= sin2θ + cosec2θ + 2sinθ cosecθ + cos2θ + sec2θ + 2cosθ secθ
= (sin2θ + cos2θ) + cosec2θ + 2 + sec2θ + 2
= 1 + (1 + cot2θ) + 2 + (1 + tan2θ) + 2
= tan2θ + cot2θ + 7
= R.H.S.
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