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).