if 2cos2θ – 5cos θ + 2 = 0, 0° < θ < 90°, then the value of (cosec θ + cot θ) is?
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Correct answer: D
Explanation
The correct answer is option 4 i.e. √3.
cosθ ≤ 1 (Always)
cos60° = 1/2
cosec60° = 2/√3
cot60° = 1/√3
Given
2cos2θ - 5cosθ + 2 = 0
2cos2θ - 5cosθ + 2 = 0
⇒ 2cos2θ - 4cosθ - cosθ + 2 = 0
⇒ 2cosθ(cosθ – 2) – 1(cosθ – 2)
⇒ (cosθ – 2)(2cosθ – 1)
⇒ cosθ = 1/2 or 2
Since cosθ ≤ 1
Hence, cosθ = 1/2
θ = 60°
Hence,
cosecθ + cotθ = 2/√3 + 1/√3 = √3