If $2 \sin A = 1$, then the value of $ an A + \cot A$ is :

Question

If $2 \sin A = 1$, then the value of $	an A + \cot A$ is :

Accepted Answer

**Step 1 — Find angle A.**
$$2\sin A = 1 \ \Rightarrow\ \sin A = \frac{1}{2} \ \Rightarrow\ A = 30^\circ$$

**Step 2 — Write the required ratios.**
$$	an 30^\circ = \frac{1}{\sqrt3}, \qquad \cot 30^\circ = \sqrt3$$

**Step 3 — Add them.**
$$	an A + \cot A = \frac{1}{\sqrt3} + \sqrt3 = \frac{1 + 3}{\sqrt3} = \frac{4}{\sqrt3}$$

**Answer : (B) $\dfrac{4}{\sqrt3}$**