Question

The value of $\tan {20}^{\circ }\tan {80}^{\circ }\cot {50}^{\circ }$ is

• A. $\sqrt{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{\sqrt{3}}{4}$
• D. $\frac{1}{2\sqrt{3}}$

Answer 1

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

$\tan {20}^{\circ }\tan {80}^{\circ }\cot {50}^{\circ }=\tan {20}^{\circ }\tan {80}^{\circ }\tan {40}^{\circ }=\tan {20}^{\circ }\tan ({60}^{\circ }+{20}^{\circ })\tan ({60}^{\circ }-{20}^{\circ })=\tan 3\left({20}^{\circ }\right)=\sqrt{3}$