The value of
Question:

The value of $\tan ^{-1} 2+\tan ^{-1} 3$ is___________________.

Solution:

We know

$\tan ^{-1} x+\tan ^{-1} y=\pi+\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$, if $x y>1$

$\therefore \tan ^{-1} 2+\tan ^{-1} 3$

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

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

$=\pi-\frac{\pi}{4}$

$=\frac{3 \pi}{4}$

The value of $\tan ^{-1} 2+\tan ^{-1} 3$ is

$\frac{3 \pi}{4}$

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