Question

If senX + cosX =p and secX + cosecX = q ,then find q÷p ×(p2-1)

Answer 1

Question should be "If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p"Solution: Consider, secθ + cosecθ = q ⇒ [(1/sinθ) + (1/cosθ)] = q ⇒ [(sinθ + cosθ)/sinθcosθ] = q ⇒ [p/sinθcosθ] = q ⇒ sinθcosθ = p/q → (1) Consider, sinθ + cosθ = p Squaring on both the sides we get (sinθ + cosθ)2 = p2 ⇒ sin2θ + cos2θ + 2sinθcosθ = p2⇒ 1 + 2(p/q) = p2  [From (1)] ⇒ (q + 2p)/q = p2  ⇒ (q + 2p) = p2q ⇒ 2p = p2q – q ⇒ 2p = q(p2 – 1)