SSC Selection Post 2022 PYQ — Question 74

The correct answer is option 1 i.e. $\sqrt2$ + 1.

7cos²θ + 5sin²θ - 6 = 0 (0° < θ < 90°)

⇒ 7(1 - sin²θ) + 5sin²θ - 6 = 0

⇒ 7 - 7sin²θ + 5sin²θ - 6 = 0

⇒ sin²θ = 1/2

⇒ sinθ = 1/√2

⇒ θ = 45°

Now, $\sqrt{{cosec θ+cot θ}\over{cosec θ-cot θ}}$

= √[(√2 + 1)/(√2 - 1)]

= √[(√2 + 1)²]

= √2 + 1