Question

If α + β = 90° and α = 2β, then the value of 3 cos² α - 2 sin² β is equal to:
1. 3 / 4
2. 1 / 4
3. 4 / 3
4. 3 / 2

Answer 1

Correct Answer - Option 2 : 1 / 4

Given - 

α + β = 90° and α = 2β

Solution - 

α + β = 90° and α = 2β

⇒ 2β + β = 90° 

⇒ β = 30° 

⇒ α = 60° 

⇒ 3 cos2 α - 2 sin2 β = 3 cos²60° - 2 sin²30° 

⇒ 3 cos2 α - 2 sin2 β = 3 × (1/4) - 2 × (1/4) = (1/4)

∴ 3 cos2 α - 2 sin2 β = (1/4).