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Question
Find the acute angle θ such that 2 cos2θ = 3 sin θ.
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Solution
2 cos2 θ = 3 sin θ
∴ 2(1 – sin2θ) = 3 sin θ
∴ 2 – 2 sin2θ = 3 sin θ
∴ 2 sin2 θ + 3sin θ – 2 = 0
∴ 2 sin2 θ + 4 sin θ – sin θ – 2 = 0
∴ 2 sin θ (sin θ + 2) –1 (sin θ + 2) = 0
∴ (sin θ + 2) (2 sin θ – 1) = 0
∴ sin θ + 2 = 0 or 2 sin θ – 1 = 0
∴ sin θ = – 2 or sin θ = `1/2`
Since, – 1 ≤ sin θ ≤ 1
∴ sin θ = `1/2`
∴ θ = 30° ...`[because sin 30^circ = 1/2]`
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