If 2cos² θ -5cos θ +2 = 0,0° θ 1/((cosecθ +cotθ)) is:

If 2cos² $\theta$ -5cos $\theta$ +2 = 0,0°< $\theta$ < 90°, then the value of $\frac{1}{(cosec\theta +cot\theta)}$ is:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. √3/3.

Given: 2cos²θ − 5cosθ + 2 = 0

Solve: (2cosθ − 1)(cosθ − 2) = 0
⇒ cosθ = 1/2 ⇒ θ = 60°

Find: 1 / (cotθ + cosecθ)
⇒ cot60° = 1/√3, cosec60° = 2/√3
⇒ Sum = 3/√3 = √3

Final: 1 / √3 = √3/3

SSC Selection Post 2020 PYQ — Question 57