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

The value of $\tan ^{-1} 2+\tan ^{-1} 3$ is
  1. $\left(\frac{3 \pi}{4}\right)^c$
  2. $\left(\frac{\pi}{2}\right)^c$
  3. $\left(\frac{\pi}{4}\right)^c$
  4. $\left(\frac{\pi}{6}\right)^c$

Solution

$\begin{aligned} & \tan ^{-1} 2+\tan ^{-1} 3 \\ & =\tan ^{-1}\left[\frac{2+3}{1-(2)(3)}\right]=\tan ^{-1}\left(\frac{5}{1-6}\right)=\tan ^{-1}(-1)=\left(\frac{3 \pi}{4}\right)^c\end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 2)

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