Question

If cos theta + sin theta =root 3 cos theta , show that cos theta - sin theta =root 2 sin theta

Answer 1

Correct Question

→ If cos∅ + sin∅ = √2 cos∅, show that cos∅ - sin∅ = √2 sin∅.

Given

→ cos∅ + sin∅ = √2 cos∅

Proof

→sin∅ = √2 cos∅ - cos∅

→ sin∅ = (√2 - 1)cos∅

→ sin∅/(√2 - 1) = cos∅

On rationalizing we get,

→ sin∅(√2 + 1)/(2 - 1) = cos∅

→ sin∅(√2 + 1) = cos∅

→ √2 sin∅ + sin∅ = cos∅

→ cos∅ - sin∅ = √2 sin∅

Hence Proved.