Question : If $\tan (90-\theta)=\frac{2}{\sqrt{3}}$, then the value of $2 \sqrt{3} \tan \theta+1$ is:
Option 1: 4
Option 2: 5
Option 3: 3
Option 4: 6
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Correct Answer: 4
Solution :
$\tan (90-\theta)=\frac{2}{\sqrt{3}}$
⇒ $\cot \theta=\frac{2}{\sqrt{3}}$
⇒ $\tan \theta=\frac{\sqrt3}{2}$
$\therefore 2 \sqrt{3} \tan \theta+1=3+1=4$
Hence, the correct answer is 4.
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