First slide

Properties of ITF

Question

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

Moderate

A

0
B

1
C

$π$
D

$- π$

Solution

We have,
$\begin{array}{l} \tan^{- 1} 1 + \tan^{- 1} 2 + \tan^{- 1} 3 \\ = \tan^{- 1} 1 + π + \tan^{- 1} (\frac{2 + 3}{1 - 2 \times 3}) \\ = \tan^{- 1} 1 + π + \tan^{- 1} (- 1) = π \end{array}$

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