If 4 – 2sin2θ – 5cos θ = 0, 0° < θ < 90°, then the value of sin θ + tan θ is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 3√3/2
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Concept |
Understanding |
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Sin2θ = 1 – cos2θ
Cos θ is always less than or equal to 1 |
Given that: 4 – 2sin2θ – 5 cosθ = 0 Using Sin2θ = 1 – cos2θ: ⇒ 4 – 2(1 - cos2θ) – 5cos θ = 0 ⇒ 2cos2θ - 5cos θ + 2 = 0 ⇒ 2cos2θ - 4cos θ - cos θ + 2 = 0 ⇒ 2cosθ (cosθ – 2) –1(cosθ – 2) ⇒ (2cosθ – 1) (cosθ – 2) ⇒ cos θ = 2, 1/2 (cos θ cannot be 2) so, cos θ = 1/2 ⇒ θ = 60° Hence, sin θ + tan θ = √3/2 + √3 ⇒ 3√3/2 |