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

Question

Philoid · Accepted Answer

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 = p²

⇒ sin² θ + cos² θ + 2 sin θ cos θ = p²

⇒ 1+2 sin θ cos θ = p² [∵,sin² θ + cos² θ = 1]

⇒ q+2p = p² q

⇒ q (p² – 1) = 2p

Hence, proved.