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SSC CGL 2025 PYQ — Question 53

SSC CGL - 18 Sep 2025 - Shift 3 • Quantitative Aptitude • Q53

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If sin⁡A=2x1+x2\sin A = \frac{2x}{1+x^2}, what is cos A?

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Correct answer: B

Explanation

The correct answer is Option 2 i.e.1−x21+x2\frac{1-x^2}{1+x^2}.

cos⁡2A=1−sin⁡2A=1−(2x1+x2)2\cos^2 A = 1 - \sin^2 A = 1 - \left( \frac{2x}{1+x^2} \right)^2

=1−4x2(1+x2)2= 1 - \frac{4x^2}{(1+x^2)^2}

=(1+x2)2−4x2(1+x2)2= \frac{(1+x^2)^2 - 4x^2}{(1+x^2)^2}

=1+2x2+x4−4x2(1+x2)2= \frac{1 + 2x^2 + x^4 - 4x^2}{(1+x^2)^2}

=1−2x2+x4(1+x2)2= \frac{1 - 2x^2 + x^4}{(1+x^2)^2}

=(1−x2)2(1+x2)2= \frac{(1 - x^2)^2}{(1+x^2)^2}

⇒ cos⁡A=1−x21+x2\cos A = \frac{1 - x^2}{1 + x^2}