Question

If $\tan (x+y)=33$ and $x={\tan }^{-1}3$ , then $y$ will be

• A. $0.3$
• B. ${\tan }^{-1}(1.3)$
• C. ${\tan }^{-1}(0.3)$
• D. ${\tan }^{-1}\left(\frac{1}{18}\right)$

Answer 1

Answer: (C)

Given, $\tan (x+y)=33$
$\Rightarrow$ $x+y={\tan }^{-1}(33)$
$\Rightarrow$ $y={\tan }^{-1}(33)-x$
$[\because x={\tan }^{-1}(3)]$
$\Rightarrow$ $y={\tan }^{-1}(33)-{\tan }^{-1}(3)$ (given)
$\Rightarrow$ $y={\tan }^{-1}\left(\frac{33-3}{1+33.3}\right)={\tan }^{-1}\left(\frac{30}{100}\right)$
$={\tan }^{-1}(0.3)$