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SSC CGL 2023 PYQ — Question 52

SSC CGL - 19 July 2023 - Shift 1 • Quantitative Aptitude • Q52

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If (cosA1−sinA)+(cosA1+sinA)=4\left ( \frac{cosA}{1-sinA} \right )+\left ( \frac{cosA}{1+sinA} \right )=4, then what will be the value of A? (0° < θ < 90°)

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 60°

Given that

If (cosA1−sinA)+(cosA1+sinA)=4\left ( \frac{cosA}{1-sinA} \right )+\left ( \frac{cosA}{1+sinA} \right )=4,

⇒ (cosA(1+sinA)+cosA(1−sinA)1−sin2A)=4\left (\frac{cosA(1+sinA) + cos A(1 - sinA)}{1-sin^2A} \right )=4

⇒ (cosA+cosAsinA+cosA−cosAsinAcos2A)=4\left (\frac{cosA+cosAsinA + cos A -cosA sinA}{cos^2A} \right )=4

⇒ 2/cosA = 4

⇒ cos A = 1/2 = cos 60°

⇒ A = 60°