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(13) = tan(11+2)

tan (13) $=\frac{tan11+tan2}{1-tan11.tan2}$ $\because tan(A+B)=\frac{tanA+tanB}{1-tanA.tanB}$

$tan13-tan11.tan2.tan13=tan11.+tan2$

$\therefore tan11+tan2-tan13=-tan11.tan2.tan13---\left(1\right)$

$\frac{tan2+tan11-tan13}{tan2.tan11.tan13}=-1$