If sin θ +cos θ =p and sec θ +cosec θ =q, then prove that q(p^{2} - 1)=2p.

Given that sin θ + cos θ = p and sec θ + cosec θ = q

Taking sec θ + cosec θ = q

Squaring sin θ + cos θ = p,

We have (sin θ + cos θ)^{2} = p^{2}

⇒ sin^{2} θ + cos^{2} θ + 2 sin θ cos θ = p^{2}

⇒ 1+2 sin θ cos θ = p^{2} [∵,sin^{2} θ + cos^{2} θ = 1]

⇒ q+2p = p^{2} q

⇒ q (p^{2} – 1) = 2p

Hence, proved.

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