SSC CGL 2021 PYQ — Question 61

The correct answer is option 4 i.e. $\frac{1}{9}$

Given :

$\frac{cosec \theta + cot \theta}{cosec \theta - cot \theta} = 7$

Calculations :

⇒ cosec θ + cot θ = 7(cosec θ - cot θ)

⇒ 8 cot θ = 6 cosec θ

⇒ 8 (cos θ/sin θ) = 6 (1/sin θ)

⇒ cos θ = 3/4

Using trigonometric ratios, we get

⇒ sin θ = $\sqrt{7}/4$

Now we have, $\frac{4sin^2\theta - 1}{4sin^2\theta + 5}$

Putting the value of sin θ, we get

⇒ (4(7/16) - 1)/(4(7/16) + 5)

⇒ (3/4)/(27/4)

⇒ 1/9