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SSC CHSL 2023 PYQ — Question 54

SSC CHSL - 09 March 2023 - Shift 2 • Quantitative Aptitude • Q54

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Simplify:1−sin⁡A1+sin⁡A\sqrt{\frac{1-\sin A}{1+\sin A}}?

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. sec A - tan A.

1−sin⁡A1+sin⁡A\sqrt{\frac{1-\sin A}{1+\sin A}}

=1−sin⁡A1+sin⁡A×1−sin⁡A1−sin⁡A=\sqrt{\frac{1-\sin A}{1+\sin A}} \times \sqrt{\frac{1-\sin A}{1-\sin A}}

=(1−sin⁡A)21−sin⁡2A= \sqrt{\frac{(1-\sin A)^2}{1 - \sin^2 A}}

=(1−sin⁡A)2cos⁡2A= \sqrt{\frac{(1-\sin A)^2}{\cos^2 A}}

=1−sin⁡Acos⁡A= \frac{1-\sin A}{\cos A}

= sec A - tan A