Question

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

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

Answer 1

Answer: (C)

${tan}^{-1}\left(0.3\right)$

Given,

$\tan (x+y)=33$

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

$\Rightarrow \tan x=3$

Formula,

$\tan (x+y)=\frac{\tan x+\tan y}{1-\tan x\tan y}$

$33=\frac{3+\tan y}{1-\left(3\right)\tan y}$

$33(1-3\tan y)=3+\tan y$

$33-99\tan y=3+\tan y$

$30=100\tan y$

$\tan y=\frac{30}{100}=0.3$

$\therefore y={\tan }^{-1}0.3$