Question

17. 2 cos? 0 + V2 sin0 = 2​

Answer 1

Answer:

Correct Question

If cos∅ + sin∅ = √2 cos∅, then prove that cos∅ - sin∅ = √2 sin∅.

Proof

→ cos∅ + sin∅ = √2 cos∅

→ sin∅ = √2 cos∅ - cos∅

→ sin∅ = cos∅(√2 - 1)

→ sin∅/(√2 - 1) = cos∅

On rationalizing we get,

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

→ sin∅(√2 + 1)/(2 - 1) = cos∅

→ √2 sin∅ + sin∅ = cos∅

→ √2 sin∅ = cos∅ - sin∅

Or cos∅ - sin∅ = √2 sin∅

Hence Proved