Question : If $\tan \frac{\pi}{6}+\sec\frac{\pi}{6}=x$, then find $x$.
Option 1: $\sqrt{3}$
Option 2: $\frac{1}{\sqrt{3}}$
Option 3: $\frac{-1}{\sqrt{3}}$
Option 4: $\frac{2}{\sqrt{3}}$
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Correct Answer: $\sqrt{3}$
Solution : Given: $\tan \frac{\pi}{6}+\sec\frac{\pi}{6}=x$ ⇒ $\tan30^\circ+\sec30^\circ=x$ ⇒ $x=\frac{1}{\sqrt{3}}+\frac{2}{\sqrt{3}}$ ⇒ $x=\frac{3}{\sqrt{3}}$ $\therefore x =\sqrt{3}$ Hence, the correct answer is $\sqrt{3}$.
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