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SSC CHSL 2025 PYQ — Question 73

SSC CHSL - 14 Nov 2025 - Shift 1 • Quantitative Aptitude • Q73

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Simplify:1+sin⁡x1−cos⁡x+1−sin⁡x1+cos⁡x\frac{1+\sin x}{1-\cos x} + \frac{1-\sin x}{1+\cos x}

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Correct answer: B

Explanation

Has been given :

1+sin⁡x1−cos⁡x+1−sin⁡x1+cos⁡x\frac{1+\sin x}{1-\cos x} + \frac{1-\sin x}{1+\cos x}

According to the formula:

(1 − cos x)(1 + cos x) = 1 − cos²x = sin²x

LCM = (1 − cos x)(1 + cos x)

[(1 + sin x)(1 + cos x) + (1 − sin x)(1 − cos x)] / [(1 − cos x)(1 + cos x)]

= [1 + cos x + sin x + sin x cos x + 1 − cos x − sin x + sin x cos x] / sin²x

= (2 + 2 sin x cos x) / sin²x

= 2(1 + sin x cos x) / sin²x