Question : The value of $\tan 5^{\circ} \tan 25^{\circ} \tan 45^{\circ} \tan 65^{\circ} \tan 85^{\circ}$ is ______.
Option 1: 4
Option 2: 3
Option 3: 1
Option 4: 2
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Correct Answer: 1
Solution :
$\tan 5^{\circ} \tan 25^{\circ} \tan 45^{\circ} \tan 65^{\circ} \tan 85^{\circ}$
$=\tan 5^{\circ} \tan (90^{\circ} - 5^{\circ})\tan 25^{\circ} \tan (90^{\circ} - 25^{\circ}) \tan 45^{\circ}$
$=\tan 5^{\circ} \cot 5^{\circ}\tan 25^{\circ} \cot 25^{\circ} \times 1$
$=1 \times 1\times 1$
$= 1$
Hence, the correct answer is 1.
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