Question

If sin 5θ = x, then find the value of (cos 8θ cos 2θ – sin 8θ sin 2θ).
1. 1 + x²
2. 1 – x²
3. 1 + 2x²
4. 1 – 2x²

Answer 1

Correct Answer - Option 4 : 1 – 2x²

As we know, cos (A + B) = cos A cos B – sin A sin B

⇒ (cos 8θ cos 2θ – sin 8θ sin 2θ)

= cos (8θ + 2θ)

= cos 10θ

∵ cos 2A = 1 – 2 sin² A

= 1 – 2 sin² 5θ

= 1 – 2x²