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SSC CHSL 2025 PYQ — Question 75

SSC CHSL - 13 Nov 2025 - Shift 3 • Quantitative Aptitude • Q75

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cos⁡x1+sin⁡x+sin⁡x1+cos⁡x=?\frac{\cos x}{1 + \sin x} + \frac{\sin x}{1 + \cos x} =?

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Correct answer: D

Explanation

Has been given :
cos(x)/(1 + sin x) + sin(x)/(1 + cos x)
According to the formula:
LCM = (1 + sin x)(1 + cos x)
[cos x(1 + cos x) + sin x(1 + sin x)] / [(1 + sin x)(1 + cos x)]
= [cos x + cos²x + sin x + sin²x] / [(1 + sin x)(1 + cos x)]
= [cos x + sin x + (sin²x + cos²x)] / [(1 + sin x)(1 + cos x)]
= [cos x + sin x + 1] / [(1 + sin x)(1 + cos x)]