Question

Prove the following trigonometric identities.

If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ − 3 cos θ = ± 3.

Answer 1

Given:

We have to prove that 5sin θ – 3cos θ = ±3.

We know that,

Squaring the given equation, we have

⇒ (5sin θ – 3cos θ)² = 9
⇒ 5sin θ – 3cos θ = ±3

Hence proved.