Question

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

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{3}$
• C. ${\text{tan}}^{-1}\left(0.3\right)$
• D. ${\text{tan}}^{-1}\left(\frac{1}{18}\right)$

Answer 1

The correct option is C ${\text{tan}}^{-1}\left(0.3\right)$

$\tan (x+y)=33$
$\Rightarrow x+y={\text{tan}}^{-1}33$
$\Rightarrow y={\text{tan}}^{-1}33-{\text{tan}}^{-1}3$
$\Rightarrow y={\text{tan}}^{-1}\left(\frac{33-3}{1+33\cdot 3}\right)$
$\Rightarrow y={\tan }^{-1}\left(\frac{30}{100}\right)$
$\therefore y={\text{tan}}^{-1}\left(0.3\right)$