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SSC CHSL 2025 PYQ — Question 72

SSC CHSL - 13 Nov 2025 - Shift 2 • Quantitative Aptitude • Q72

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Simplify:(sin⁡(x)+cos⁡(x))21+sin⁡(x)cos⁡(x)\frac{(\sin(x) + \cos(x))^2}{1 + \sin(x)\cos(x)}

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Correct answer: D

Explanation

(sin⁡(x)+cos⁡(x))21+sin⁡(x)cos⁡(x)\frac{(\sin(x) + \cos(x))^2}{1 + \sin(x)\cos(x)}
According to the formula:
(a + b)² = a² + b² + 2ab
sin²x + cos²x = 1
(sin x + cos x)²= sin²x + cos²x + 2sin x cos x
= 1 + 2sin x cos x
(1 + 2sin x cos x) / (1 + sin x cos x)