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SSC CGL 2023 PYQ — Question 74

SSC CGL - 19 July 2023 - Shift 3 • Quantitative Aptitude • Q74

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If 2 cot x = 5, then what is 2cos⁡x−sin⁡x2cos⁡x+sin⁡x\frac{2 cos⁡x-sin⁡x}{2 cos⁡x+sin⁡x } equal to?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 23\frac{2}{3}.

Given that

If 2 Cot x = 5,

cot x = 5/2

According to the question

= 2cos⁡x−sin⁡x2cos⁡x+sin⁡x\frac{2 cos⁡x-sin⁡x}{2 cos⁡x+sin⁡x }

= sinx(2cot⁡x−1)sinx(2cotx+1)\frac{sinx(2 cot⁡x-1)}{sinx(2 cot x+1)}

= (2cot⁡x−1)(2cotx+1)\frac{(2 cot⁡x-1)}{(2 cot x+1)}

= (2 × 5/2 -1)/(2 × 5/2 +1)

= 4/6

= 23\frac{2}{3}