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SSC CHSL 2023 PYQ — Question 63

SSC CHSL - 14 Aug 2023 - Shift 3 • Quantitative Aptitude • Q63

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The value of 1+sinAcosA+cosA1+sinA\frac{1 + sinA}{cosA} + \frac{cosA}{1 + sinA} is:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 2 secA.

1+sinAcosA+cosA1+sinA\frac{1 + sinA}{cosA} + \frac{cosA}{1 + sinA}

=(1+sin⁡A)2+cos⁡2Acos⁡A(1+sin⁡A)= \frac{(1 + \sin A)^2 + \cos^2 A}{\cos A (1 + \sin A)}

=1+2sin⁡A+sin⁡2A+cos⁡2Acos⁡A(1+sin⁡A)= \frac{1 + 2 \sin A + \sin^2 A + \cos^2 A}{\cos A (1 + \sin A)}

=1+2sin⁡A+1cos⁡A(1+sin⁡A)= \frac{1 + 2 \sin A + 1}{\cos A (1 + \sin A)}

=2(1+sin⁡A)cos⁡A(1+sin⁡A)= \frac{2(1 + \sin A)}{\cos A (1 + \sin A)}

= 2/cosA

= 2secA