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Question
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
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Solution
q(p2 – 1) = (sec A + cosec A) [(sin A + cos A)2 – 1]
= (sec A + cosec A) [(sin2 A + cos2 A + 2 sin A cos A) – 1]
= (sec A + cosec A) [(1 + 2 sin A cos A) – 1]
= (sec A + cosec A) (2 sin A cos A)
= 2 sin A + 2 cos A
= 2p
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