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SSC CGL 2025 PYQ — Question 52

SSC CGL - 22 Sep 2025 - Shift 1 • Quantitative Aptitude • Q52

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If sin A = mn\frac{m}{n} and A ∈\in (0, π/2), then what is cos A in terms of m and n?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. n2−m2n\frac{\sqrt{n^2 - m^2}}{n}.

sin2A + cos2A = 1

⇒ (mn)2+cos⁡2A=1\left(\frac{m}{n}\right)^2 + \cos^2 A = 1

⇒ m2n2+cos⁡2A=1\frac{m^2}{n^2} + \cos^2 A = 1

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

⇒ cos⁡A=n2−m2n2=n2−m2n\cos A = \sqrt{\frac{n^2 - m^2}{n^2}} = \frac{\sqrt{n^2 - m^2}}{n}