### Question 23

SSC-CGL 2020 Mar 3 Shift 2

If sinθ = 1/4, then the value of 8(cosθ + cotθ) is?

### Solution in Detail

Given $\displaystyle \sin \theta = \frac 14$

$\displaystyle \therefore H = 4, P = 1$

so $\displaystyle B = \sqrt{4^2 - 1} = \sqrt {15}$

$\displaystyle \implies \cos \theta = \frac BH = \frac{\sqrt {15}}{4}$

$\displaystyle \cot \theta = \frac BP= \frac{\sqrt {15}}{1} = \sqrt {15}$

$\displaystyle \therefore 8(\cos \theta + \cot \theta)$

$\displaystyle = 8\bigg(\frac{\sqrt {15}}{4} + \sqrt {15}\bigg)$

$\displaystyle =10\sqrt{15}\:\underline{Ans}$

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