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$\tan 12 ° . \tan 24 ° . \tan 48 ° . \tan 84 ° =$

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\frac{1}{\sqrt{3}}

- 1

\sqrt{3}

answer is A.

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Detailed Solution

\tan θ . \tan (60 - θ) . \tan (60 + θ) = \tan 3 θ

$= \frac{\tan 12. \tan (60 - 12) . \tan (60 + 12) \tan 24. \tan (60 - 24) \tan (60 + 24)}{\tan (60 + 12) \tan (60 - 24)}$

$= \frac{\tan 3 (12) . \tan 3 (24)}{\tan 72. \tan 36}$

$= \frac{\tan 36. \tan 72}{\tan 72. \tan 36}$

$= 1$

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