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SSC CHSL 2022 PYQ — Question 71

SSC CHSL - 3 June 2022 - Shift 2 • Quantitative Aptitude • Q71

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If 1 + tan θ=3\theta=\sqrt{3}, then 3\sqrt{3} cot θ\theta - 1 = _______.

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Correct answer: A

Explanation

The correct answer is option 1 i.e.  3+12\frac{\sqrt{3}+1}{2}

 1 + tan θ=3\theta=\sqrt{3}

 tan θ=3\theta=\sqrt{3} - 1

cotθ\theta = 13−1×3+13+1\frac{1}{\sqrt3-1}\times\frac{\sqrt3+1}{\sqrt3+1}

cotθ\theta = 3+12\frac{\sqrt3+1}{2}

So, the value of  3\sqrt{3} cot θ\theta - 1 =   3\sqrt{3}  3+12\frac{\sqrt3+1}{2}- 1

= (3 + 3\sqrt{3} - 2)/2

= 3+12\frac{\sqrt{3}+1}{2}