If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p. - Mathematics

If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p² – 1) = 2p.

Sum

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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