If 2 sin2θ + 5 cos θ – 4 = 0, 0° < θ < 90°, then the value of cot θ + cosec θ is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. √3
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Concept |
Understanding |
Application |
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Cosx is always less than or equal to 1. Cos 60° = 1/2 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, 1/2 But cosθ can’t be equal 2 Hence, Cos θ = 1/2 θ = 60° Now, Cot θ + Cosec θ = 1/√3 + 2/√3 = (1 + 2)/√3 = 3/√3 = √3 |