Question

The value $\tan {100}^{\circ }+\tan {125}^{\circ }+\tan {100}^{\circ }\tan {125}^{\circ }$ is

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

Answer 1

The correct option is B $1$

We know that,
$\tan \left({225}^{\circ }\right)=\tan ({100}^{\circ }+{125}^{\circ })\Rightarrow 1=\frac{\tan {100}^{\circ }+\tan {125}^{\circ }}{1-\tan {100}^{\circ }\tan {125}^{\circ }}\Rightarrow \tan {100}^{\circ }+\tan {125}^{\circ }+\tan {100}^{\circ }\tan {125}^{\circ }=1$