Question

The value of $\frac{\tan {70}^{\circ }-\tan {20}^{\circ }}{\tan {50}^{\circ }}$ is

• A. $2$
• B. $1$
• C. $0$
• D. $\infty$

Answer 1

The correct option is A $2$

$\frac{\tan {70}^{\circ }-\tan {20}^{\circ }}{\tan {50}^{\circ }}$
$=\frac{\tan {70}^{\circ }-\tan {20}^{\circ }}{\tan (70-20{)}^{\circ }}$
$=\frac{\tan {70}^{\circ }-\tan {20}^{\circ }}{\tan {70}^{\circ }-\tan {20}^{\circ }}\times (1+\tan {70}^{\circ }\tan {20}^{\circ })$
$=1+\tan {70}^{\circ }\tan {20}^{\circ }$
$=1+\tan {70}^{\circ }\cot {70}^{\circ }$
$=1+1=2$