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. ${\tan }^{-1}\frac{1}{18}$

Answer 1

The correct option is C

${\tan }^{-1}0.3$

Explanation for correct option:

Step 1: Apply Trigonometric identities

$\tan (x+y)=33$ …..(i)

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

$\Rightarrow \tan x=3$ …..(iI)

Formula,

$\tan \left(x+y\right)=\frac{\tan x+\tan y}{1-\tan x\tan y}$ …..(iiI)

Step 2: Putting the Value of equations (i) and (ii) in equation (iii)

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

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

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

$\Rightarrow 30=100\tan y$

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

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

Hence Option (3) is Correct