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SSC CGL 2025 PYQ — Question 59

SSC CGL - 25 Sep 2025 - Shift 3 • Quantitative Aptitude • Q59

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If cosecA - sin A = 2, then find the value of sin A.

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Correct answer: A

Explanation

The correct answer is option 1 i.e.  -1 + 2\sqrt{2}.

cosec A – sin A = 2

⇒ (1/sin A) – sin A = 2

⇒ 1 – sin2A = 2 sin A

⇒ sin2A + 2 sin A – 1 = 0

⇒ sin A =−2±4+42=−2±82=−2±222=−1±2= \frac{-2 \pm \sqrt{4 + 4}}{2} = \frac{-2 \pm \sqrt{8}}{2} = \frac{-2 \pm 2\sqrt{2}}{2} = -1 \pm \sqrt{2}