If sinθ.sin45° = sin30° and θ is an acute angle, then 2θ is equal to:
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 90°.
sinθ.sin45° = sin30°
⇒ sinθ × (1/√2) = (1/2)
⇒ sinθ = (1/2) × √2 = 1/√2
⇒ sinθ = sin45°
⇒ θ = 45°
⇒ 2θ = 2 × 45° = 90°
Therefore, the value of 2θ is 90°.