Question : If $\mathrm{A}=\cot 30^{\circ} \tan 60^{\circ}+\cot 60^{\circ} \tan 30^{\circ}$, then what is the value of A?
Option 1: $\frac{1}{ \sqrt{ 3}}$
Option 2: $\frac{10}{3}$
Option 3: $\frac{10}{ \sqrt{3}}$
Option 4: $\frac{1}{3}$
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Correct Answer: $\frac{10}{3}$
Solution :
Given, $\mathrm{A}=\cot 30° \tan 60°+\cot 60° \tan 30°$
Putting values, we get,
$=\sqrt3×\sqrt3+\frac{1}{\sqrt3}×\frac{1}{\sqrt3}$
$=3+\frac{1}{3}$
$=\frac{10}{3}$
Hence, the correct answer is $\frac{10}{3}$.
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