Question

Prove ${\tan }^{-1}\frac{2}{11}+{\tan }^{-1}\frac{7}{24}={\tan }^{-1}\frac{1}{2}$

Answer 1

${\tan }^{-1}\frac{2}{11}+{\tan }^{-1}\frac{7}{24}$

$={\tan }^1\left(\frac{\frac{2}{11}+\frac{7}{24}}{1-\frac{2}{11}\times \frac{7}{24}}\right)$

$={\tan }^{-1}\left(\frac{48+77}{264-14}\right)$

$={\tan }^{-1}\left(\frac{125}{250}\right)$

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