Question

Solve: ${\tan }^{-1}\left[\frac{6x}{1-{5x}^2}\right]$

Answer 1

We have,

$y={\tan }^{-1}\left[\frac{6x}{1-5x^2}\right]$

$={\tan }^{-1}\left[\frac{5x+x}{1-5x^2}\right]$

$={\tan }^{-1}\left(5x\right)+{\tan }^{-1}x\therefore {\tan }^{-1}A+{\tan }^{-1}B={\tan }^{-1}\left(\frac{A+B}{1-AB}\right)$

Hence, this is the answer.