Question

If Sin + Cos = p and Sec + Cosec = q , show that q ( p 2 – 1) = 2 p.

Answer 1

go through the solution step by step

Answer 2

Solution

→ p = sin∅ + cos∅

→ p² = (sin∅ + cos∅)²

→ p² = sin²∅ + cos² + 2 sin∅ cos∅

→ p² = 1 + 2 sin∅ cos∅

→ p² - 1 = 2 sin∅ cos∅

→ q = sec∅ + cosec∅

→ q = 1/cos∅ + 1/sin∅

→ q = (sin∅ + cos∅)/cos∅ sin∅

→ q(p² - 1) = (sin∅ + cos∅)/cos∅ sin∅ × 2 sin∅ cos∅

→ 2 (sin∅ + cos∅) → 2p

Q.E.D