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  1. If 0° < θ < 90° and 2 sin²θ + 3 cosθ = 3, then the value of θ is
    1. 30°
    2. 60°
    3. 45°
    4. 75°
Correct Option: B

2 sin²θ + 3 cos θ = 3
⇒ 2 (1–cos²θ) + 3 cos θ = 3
⇒ 2 – 2 cos²θ + 3 cos θ = 3
⇒ 2 cos²θ – 3 cos θ + 1 = 0
⇒ 2 cos²θ – 2 cos θ – cos θ + 1 = 0
⇒ 2 cos θ (cos θ – 1) –1 (cos θ – 1) = 0
⇒ (2 cos θ – 1) (cos θ – 1) = 0
⇒ 2 cos θ – 1 = 0
⇒ 2 cos θ = 1

⇒ cos θ =
1
⇒ θ = 60°
2

or, cos θ – 1 = 0
⇒ cos θ = 1
⇒ θ = 0°



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