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SSC CGL 2022 PYQ — Question 60

SSC CGL - 19 April 2022 - Shift 3 • Quantitative Aptitude • Q60

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Simplify the following expression: cos⁡A1−tan⁡A+sin⁡A1−cot⁡A−sin⁡A\dfrac{\cos A}{1-\tan A}+\dfrac{\sin A}{1-\cot A}-\sin A

 

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Correct answer: D

Explanation

The correct answer is option 4 i.e. cos A

cos⁡A1−tan⁡A+sin⁡A1−cot⁡A−sin⁡A\dfrac{\cos A}{1-\tan A}+\dfrac{\sin A}{1-\cot A}-\sin A

Put A = 30° 

⇒ {(31/2/2)}/{(31/2 - 1)/2} + {(1/2)/(1 - 31/2)} - 1/2

⇒ 3/[2 × (31/2 - 1)] - 1/[2 × (31/2 - 1)] - 1/2

⇒ 2/[2 × (31/2 - 1)] - 1/2

⇒ 1/ (31/2 - 1) - 1/2

⇒ {(31/2 + 1)/ (31/2 - 1)(31/2 + 1)} - 1/2

⇒ (31/2 + 1)/2 - 1/2

⇒ 31/2/2

From the options, when we put A = 30°, only option 4 gives us the value o