Question : What is the value of $3 \tan 20° \tan 45°\tan 70°$?
Option 1: 2
Option 2: 3
Option 3: 1.5
Option 4: 4
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Correct Answer: 3
Solution :
$3 \tan 20°\tan 45° \tan70°$
$= 3 \tan 20°\tan 45° \tan (90° - 20°)$ [Using $\tan \theta = \cot (90° - \theta)$]
$= 3 \tan 20°\tan 45°\cot 20°$
$= 3 \times \tan 45°$
$= 3 \times 1$
$= 3$
Hence, the correct answer is 3.
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