Question

What is the value of $\tan 7^{\circ }\tan {23}^{\circ }\tan {60}^{\circ }\tan {67}^{\circ }\tan {83}^{\circ }$?

• A. $\frac{1}{\sqrt{3}}$
• B. $\sqrt{3}$
• C. $1$
• D. $\infty$

Answer 1

The correct option is B $\sqrt{3}$

$\tan 7°\tan 23°\tan 60°\tan 67°\tan 83°$

$=\tan (90°-83°)\tan (90°-67°)\sqrt{3}\tan 67°\tan 83°$

$=\cot 83°.\tan 83°.\cot 67°.\tan 67°.\sqrt{3}$

$=\sqrt{3}.$

Hence, the answer is $\sqrt{3}.$