tan - 1 ( - 2 ) - tan - 1 ( 3 ) is equal to

Given that: ${\tan }^{-1}(-2)-{\tan }^{-1}\left(3\right)$

As we know that, ${\tan }^{-1}(-x)=-{\tan }^{-1}x$

$=-{\tan }^{-1}\left(2\right)-{\tan }^{-1}\left(3\right)$

$=-\left({\tan }^{-1}\right(2)+{\tan }^{-1}(3\left)\right)$

As we know that,${\tan }^{-1}\left(x\right)+{\tan }^{-1}\left(y\right) =\mathrm{\pi }+{\tan }^{-1}\left(\frac{x+y}{1-xy}\right)$when $xy>1$ .

$=-\mathrm{\pi }-{\tan }^{-1}\left(\frac{2+3}{1-2\times 3}\right)$

$=-\mathrm{\pi }-{\tan }^{-1}(-1)$

$=-\mathrm{\pi }+{\tan }^{-1}1$

$=-\frac{3\mathrm{\pi }}{4}$