Question

The value of
$\tan {130}^{\circ }.\tan {140}^{\circ }$ is equal to

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

Answer 1

The correct option is A

$1$

$\tan {130}^{\circ }.\tan {140}^{\circ }$
$=\tan ({180}^{\circ }-{50}^{\circ }).\tan ({180}^{\circ }-{40}^{\circ })$
$=(-\tan {50}^{\circ }).(-\tan {40}^{\circ })$
$=\tan {50}^{\circ }\cot {50}^{\circ }$
$=1$