Mark the tick against the correct answer in the following:

To Find: The value of $\tan ^{-1} 2+\tan ^{-1} 3$

Since we know that $\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$

$\Rightarrow \tan ^{-1} 2+\tan ^{-1} 3=\tan ^{-1}\left(\frac{2+3}{1-(2 \times 3)}\right)$

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

$=\tan ^{-1}(-1)$

Since the principle value of tan lies in the range $[0, \pi]$

$\Rightarrow \tan ^{-1}(-1)=\frac{3 \pi}{4}$