First slide

Properties of ITF

Question

If $\tan^{- 1} x + \tan^{- 1} y + \tan^{- 1} z = π,$ then $x + y + z$ is equal to

Moderate

A

$x y z$
B

0
C

1
D

$2 x y z$

Solution

We have,
$\tan^{- 1} x + \tan^{- 1} y + \tan^{- 1} z = \tan^{- 1} (\frac{x + y + z - x y z}{1 - x y - y z - z x})$
$\begin{array}{l} \Rightarrow π = \tan^{- 1} \{\frac{x + y + z - x y z}{1 - (x y + y z + z x)}\} \\ \Rightarrow x + y + z = x y z \end{array}$

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