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SSC CGL 2022 PYQ — Question 70

SSC CGL - 05 Dec 2022 - Shift 4 • Quantitative Aptitude • Q70

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1+sinA1−sinA=\sqrt{\frac{1+sinA}{1-sinA}}=___________,

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Correct answer: C

Explanation

The correct answer is option 3 i.e. secA + tanA.

 1+sinA1−sinA\sqrt{\frac{1+sinA}{1-sinA}}

=  1+sinA1−sinA×1+sinA1+sinA\sqrt{\frac{1+sinA}{1-sinA}\times\frac{1+sinA}{1+sinA}}

= (1+SinA)21−Sin2A\sqrt\frac{{(1+SinA)^2}}{1-Sin^2A}

= (1+SinA)2Cos2A\sqrt\frac{{(1+SinA)^2}}{Cos^2A}

= 1/CosA + SinA/CosA

= SecA + tanA