First slide

Properties of ITF

Question

If $\tan^{- 1} 3 + \tan^{- 1} x = \tan^{- 1} 8, then x =$

Moderate

A

5
B

$\frac{1}{5}$
C

$\frac{5}{14}$
D

$\frac{14}{5}$

Solution

We have,
$\begin{array}{l} \tan^{- 1} 3 + \tan^{- 1} x = \tan^{- 1} 8 \\ \Rightarrow \tan^{- 1} x = \tan^{- 1} 8 - \tan^{- 1} 3 \\ \Rightarrow \tan^{- 1} x = \tan^{- 1} (\frac{8 - 3}{1 + 24}) \Rightarrow x = \frac{1}{5} \end{array}$

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