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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