Question

The value of $\tan ({\tan }^{-1}\frac{1}{2}-{\tan }^{-1}\frac{1}{3})$is

• A. $\frac{5}{7}$
• B. $\frac{7}{6}$
• C. $\frac{1}{6}$
• D. $\frac{1}{7}$

Answer 1

The correct option is D $\frac{1}{7}$

$\tan [{\tan }^{-1}\frac{1}{2}-{\tan }^{-1}\frac{1}{3}]$

$=\tan \left[{\tan }^{-1}\left(\frac{\frac{1}{2}-\frac{1}{3}}{1+\frac{1}{6}}\right)\right]=\tan \left({\tan }^{-1}\frac{1}{7}\right)$
$=\frac{1}{7}[\because \tan ({\tan }^{-1}x)=x\forall x\in R]$