Question

If $\tan {70}^{\circ }=\tan {20}^{\circ }+\lambda \tan {50}^{\circ },$ then $\lambda$ is equal to

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

Answer 1

The correct option is B $2$

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