If 2 sin2θ + 5 cos θ – 4 = 0, 0° < θ < 90° ,then the valueof tan θ + sin θ is:
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e.3√3/2
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Concept |
Understanding |
Application |
Fair calculation |
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Cosx is always less than or equal to 1. Cos60 = ½ sin2θ = 1 – cos2θ
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Given 2sin2θ + 5cosθ – 4 = 0
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2sin2θ + 5cosθ – 4 = 0 ⇒2(1 – cos2θ) + 5cosθ – 4 = 0 ⇒2cos2θ – 5cosθ + 2 = 0 ⇒2cos2θ - 4cosθ - cosθ + 2 = 0 ⇒2cosθ(cosθ – 2) – 1(cosθ – 2) ⇒(2cosθ – 1) (cosθ – 2) = 0 ⇒cosθ = 2, ½ But cosθ can’t be equal 2 Hence, Cosθ = ½ θ = 60 Now, tanθ + sinθ = √3 + √3/2 = 3√3/2 |
√3 + √3/2 = (2√3 + √3)/2 = 3√3/2 |