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SSC CGL 2025 PYQ — Question 57

SSC CGL - 26 Sep 2025 - Shift 2 • Quantitative Aptitude • Q57

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If sin⁡A=2x(1+x2)\sin A = \frac{2x}{(1+x^2)}, then what is tan A in terms of x?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 2x(1−x2)\frac{2x}{(1-x^2)}.

We know: sin⁡A=2tan⁡(A/2)1+tan⁡2(A/2)\sin A = \frac{2 \tan(A/2)}{1 + \tan^2(A/2)}

So we can set tan(A/2) = x (assuming x is real)

Then sin⁡A=2x1+x2\sin A = \frac{2x}{1 + x^2}

tan⁡A=2tan⁡(A/2)1−tan⁡2(A/2)=2x1−x2\tan A = \frac{2 \tan(A/2)}{1 - \tan^2(A/2)} = \frac{2x}{1 - x^2}