Question

If ${\tan }^{-1}3+{\tan }^{-1}x={\tan }^{-1}8$, then find the value of $x$

• A. $5$
• B. $1/5$
• C. $5/14$
• D. $14/5$

Answer 1

The correct option is B $1/5$

given, ${\tan }^{-1}3+{\tan }^{-1}x={\tan }^{-1}8$

$\Rightarrow {\tan }^{-1}x={\tan }^{-1}8-{\tan }^{-1}3$

We know that

${\tan }^{-1}A-{\tan }^{-1}B={\tan }^{-1}\left(\frac{A-B}{1+AB}\right)$

$\Rightarrow {\tan }^{-1}x={\tan }^{-1}\left(\frac{8-3}{1+24}\right)$

$\Rightarrow {\tan }^{-1}x={\tan }^{-1}\left(\frac{5}{25}\right)$

$\Rightarrow {\tan }^{-1}x={\tan }^{-1}\left(\frac{1}{5}\right)$

$\therefore x=\frac{1}{5}$