Question : If $\sin A=\frac{1}{2}$, then the value of $(\tan A+\cos A)$ is:
Option 1: $\frac{2}{3 \sqrt{3}}$
Option 2: $\frac{3}{2 \sqrt{3}}$
Option 3: $\frac{5}{2 \sqrt{3}}$
Option 4: $\frac{5}{3 \sqrt{3}}$
Correct Answer: $\frac{5}{2 \sqrt{3}}$
Solution : Given: $\sin A=\frac{1}{2}$ ⇒ $\sin A=\sin 30^\circ$ ⇒ $ A= 30^\circ$ $\therefore (\tan A+\cos A)$ = $(\tan 30^\circ+\cos 30^\circ)$ = $\frac{1}{\sqrt3}+\frac{\sqrt3}{2}$ = $\frac{2+3}{2\sqrt3}$ = $\frac{5}{2\sqrt3}$ Hence, the correct answer is $\frac{5}{2\sqrt3}$.
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