$\tan 5^{\circ} \times \tan 30^{\circ} \times 4 \tan 85^{\circ}$ is equal to
(a) $\frac{4}{\sqrt{3}}$
(b) $4 \sqrt{3}$
(c) 1
(d) 4
We have to find $\tan 5^{\circ} \times \tan 30^{\circ} \times 4 \tan 85^{\circ}$
We know that
$\tan \left(90^{\circ}-\theta\right)=\cot \theta$
$\tan \theta \cot \theta=1$
$\tan 30^{\circ}=\frac{1}{\sqrt{3}}$
So
$\tan 5 \times \tan 30^{\circ} \times 4 \tan 85^{\circ}$
$=\tan \left(90^{\circ}-85^{\circ}\right) \times \tan 30^{\circ} \times 4 \tan 85^{\circ}$
$=\cot 85^{\circ} \times \tan 30^{\circ} \times 4 \tan 85^{\circ}$
$=4 \cot 85^{\circ} \times \tan 85^{\circ} \tan 30^{\circ}$
$=4 \times 1 \times \frac{1}{\sqrt{3}}$
$=\frac{4}{\sqrt{3}}$
Hence the correct option is $(a)$
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