Question : What is the value of $\sin 30^{\circ}+\cos 30^{\circ}+\tan 30^{\circ}$?
Option 1: $\frac{5+\sqrt{3}}{2 \sqrt{3}}$
Option 2: $\frac{5-\sqrt{3}}{2 \sqrt{3}}$
Option 3: $\frac{5+\sqrt{3}}{\sqrt{3}}$
Option 4: $\frac{5-\sqrt{3}}{\sqrt{3}}$
Correct Answer: $\frac{5+\sqrt{3}}{2 \sqrt{3}}$
Solution :
Given: $\sin 30^{\circ}+\cos 30^{\circ}+\tan 30^{\circ}$
Putting the values, we get:
$=\frac{1}{2}+\frac{\sqrt3}{2}+\frac{1}{\sqrt3}$
$=\frac{\sqrt3+3+2}{2\sqrt3}$
$=\frac{5+\sqrt3}{2\sqrt3}$
Hence, the correct answer is $\frac{5+\sqrt3}{2\sqrt3}$.
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