If =1 2 then =? - Vidyadip

MCQ

If $\sin\theta=\frac{1}{2}$ then $\cot\theta=?$

A
$\frac{1}{\sqrt3}$
✓
$\sqrt{3}$
C
$\frac{\sqrt3}{2}$
D
$1$

✓

Answer

Correct option: B.

$\sqrt{3}$

$\sin^2\theta+\cos^2\theta=1$
$\Rightarrow\Big(\frac{1}2{}\Big)^2+\cos^2\theta=1$
$\Rightarrow\cos^2\theta=1-\frac{1}{4}=\frac{3}{4}$
$\Rightarrow\cos\theta=\frac{\sqrt3}{2}$
$\therefore\cot\theta=\frac{\cos\theta}{\sin\theta}$
$=\frac{\frac{\sqrt3}{2}}{\frac{1}{2}}=\sqrt3$

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