Solve this
Question:

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

(a) $\frac{\sqrt{3}}{2}$

(b) 1

(c) $\sqrt{3}$

(d) $\frac{1}{\sqrt{3}}$

Solution:

Given : $\sin \theta=\frac{1}{2}$

Since, $\sin \theta=\frac{P}{H}$

$\Rightarrow P=1$ and $H=2$

Using Pythagoras theorem,

$P^{2}+B^{2}=H^{2}$

$\Rightarrow 1^{2}+B^{2}=2^{2}$

$\Rightarrow B^{2}=4-1$

$\Rightarrow B^{2}=3$

$\Rightarrow B=\sqrt{3}$

Therefore,

$\cot \theta=\frac{B}{P}=\frac{\sqrt{3}}{1}$

Hence, the correct option is (c).

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