SSC CGL 2022 PYQ — Question 58

The correct answer is option 3 i.e. 4

Calculations:

We know that sin²θ = 1 - cos²θ

⇒ 2sin²θ + 3cosθ = 3

2(1 - cos²θ) + 3cosθ = 3

Take cosθ = a

⇒ 2 - 2a² + 3a = 3

⇒ 2a² - 3a + 1 = 0

⇒ (2a - 1) (a - 1) = 0

⇒ a = 1/2, 1

⇒ cosθ = 1/2, 1 i.e. θ = 60°

Putting the value of θ, we get

⇒ sec²60 + cot²60 = 4 + 1/3 = $4\dfrac{1}{3}$