Question

The value of $\frac{\tan {70}^o-\tan {20}^o}{\tan {50}^o}$ is equal to

• A. 2
• B. 1
• C. 0
• D. 3

Answer 1

Answer: (A)

2

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

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