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SSC CGL 2023 PYQ — Question 72

SSC CGL - 24 July 2023 - Shift 3 • Quantitative Aptitude • Q72

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If cosec θ + cot θ =32=\frac{3}{2}, then what is the value of cosec θ?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 1312\frac{13}{12}.

cosec θ + cot θ = 3/2   .....(1)

We know, cosec2θ - cot2θ = 1

⇒ (cosec θ + cot θ)(cosec θ - cot θ) = 1

⇒ (3/2)(cosec θ - cot θ) = 1

⇒ cosec θ - cot θ = 2/3   .....(2)

Adding equations (1) and (2),

2cosec θ = 13/6

⇒ cosec θ = 13/12

Therefore, the value of cosec θ is 13/12.