Question

If in a triangle two angles are ${\tan }^{-1}2$ and ${\tan }^{-1}3$ then find the third angle.

Answer 1

Given in a triangle two angles are ${\tan }^{-1}2$ and ${\tan }^{-1}3$.

Then the remaining angle is

$\pi -({\tan }^{-1}2+{\tan }^{-1}3)$

$=\pi -{\tan }^{-1}\frac{2+3}{1-2.3}$

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

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

$=\frac{\pi }{4}$.