Question : What is the value of $\tan 6^{\circ} × \tan 45^{\circ} × \tan 84^{\circ}$?
Option 1: $1$
Option 2: $\tan 6^{\circ} \times \tan 39^{\circ}$
Option 3: $3$
Option 4: $\tan 6^{\circ}+\tan 45^{\circ}+\tan 84^{\circ}$
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Correct Answer: $1$
Solution :
$\tan 6^{\circ} × \tan 45^{\circ} × \tan 84^{\circ}$
= $\tan 6^{\circ} × \tan 45^{\circ} × \tan (90^{\circ}-6^{\circ})$
= $\tan 6^{\circ} × \tan 45^{\circ} × \cot 6^{\circ}$
= $\tan 6^{\circ} × \tan 45^{\circ} × \frac{1}{\tan 6^{\circ}}$
= $\tan 45^{\circ}$
= $1$
Hence, the correct answer is $1$.
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