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SSC CGL 2024 PYQ — Question 64

SSC CGL - 09 Sep 2024 - Shift 3 • Quantitative Aptitude • Q64

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If sec a + tan asec a − tan a=74{sec\ a\ +\ tan\ a\over sec\ a\ -\ tan\ a} = {7\over4} then, find the value of cosec a.

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. 11311\over3.

sec a + tan asec a − tan a=74{sec\ a\ +\ tan\ a\over sec\ a\ -\ tan\ a} = {7\over4}

⇒ 4(sec a + tan a) = 7(sec a - tan a)

⇒ 4 sec a + 4 tan a = 7 sec a - 7 tan a

⇒ 11 tan a = 3 sec a

⇒ 11 × sin a/cos a = 3 × 1/cos a

⇒ 11 sin a = 3

⇒ sin a = 3/11

Thus, 

The value of cosec a = 1/sin a = 11311\over3