Question

Prove that ${\tan }^{-1}\frac{1}{2}+{\tan }^{-1}\frac{2}{11}={\tan }^{-1}\frac{3}{4}$.

Answer 1

Now,

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

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

$={\tan }^{-1}\frac{\frac{15}{22}}{\frac{10}{11}}$

$={\tan }^{-1}\frac{15}{20}$

$={\tan }^{-1}\frac{3}{4}$.