Question

Exact value of $\frac{\tan 2^o+\tan {11}^o-\tan {13}^o}{\tan {13}^o\tan {11}^o\tan 2^o}$ is

• A. $0$
• B. $1$
• C. $-1$
• D. $noneofthese$

Answer 1

The correct option is C $-1$

$\tan ({11}^{\circ }+2^{\circ })=\tan {13}^{\circ }$

$⟹\frac{\tan {11}^{\circ }+\tan 2^{\circ }}{1-\tan {11}^{\circ }\tan 2^{\circ }}=\tan {13}^{\circ }$

$⟹\tan {11}^{\circ }+\tan 2^{\circ }=\tan {13}^{\circ }-\tan 2^{\circ }\tan {11}^{\circ }\tan {13}^{\circ }$

$⟹\tan {11}^{\circ }+\tan 2^{\circ }-\tan {13}^{\circ }=-\tan 2^{\circ }\tan {11}^{\circ }\tan {13}^{\circ }$

$⟹\frac{\tan 2^{\circ }+\tan {11}^{\circ }-\tan {13}^{\circ }}{\tan {13}^{\circ }\tan {11}^{\circ }\tan 2^{\circ }}=-1$