SSC Selection Post 2022 PYQ — Question 74

The correct answer is option 2 i.e. $2{\sqrt3}$.

6 cos²θ + cosθ = 2

⇒ 6 cos²θ + cosθ - 2 = 0

⇒ 6 cos²θ + 4cosθ - 3cosθ - 2 = 0

⇒ (3cosθ + 2)(2cosθ - 1) = 0

⇒ 2cosθ = 1

⇒ cosθ = 1/2

⇒ θ = 60°

Now, cosec θ + cotθ + tan θ

= cosec 60° + cot 60° + tan 60°

= 2/√3 + 1/√3 + √3 = 2√3