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SSC CGL 2025 PYQ — Question 61

SSC CGL - 17 Sep 2025 - Shift 3 • Quantitative Aptitude • Q61

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If sin A = m/n, then what is the value of (1 + tan2A)?

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Correct answer: A

Explanation

The correct answer is option 1 i.e.n2n2−m2\frac{n^2}{n^2 -m^2}.

1+tan⁡2A=sec⁡2A=1cos⁡2A1 + \tan^2 A = \sec^2 A = \frac{1}{\cos^2 A}

Here, sin⁡A=mn\sin A = \frac{m}{n}

⇒ cos⁡2A=1−sin⁡2A=1−m2n2=n2−m2n2\cos^2 A = 1 - \sin^2 A = 1 - \frac{m^2}{n^2} = \frac{n^2 - m^2}{n^2}

⇒ 1+tan⁡2A=1cos⁡2A=n2n2−m21 + \tan^2 A = \frac{1}{\cos^2 A} = \frac{n^2}{n^2 - m^2}