Mathematics - Matrices Question with Solution | TestHub

$\begin{array}{rl}& 2{\tan }^{-1}\frac{1}{5}+{\tan }^{-1}\frac{1}{2}+2{\tan }^{-1}\frac{1}{8}\\ & =2{\tan }^{-1}\frac{\frac{1}{5}+\frac{1}{8}}{1-\frac{1}{5}\cdot \frac{1}{8}}+{\tan }^{-1}\frac{1}{7}\\ & =2{\tan }^{-1}\frac{1}{3}+{\tan }^{-1}\frac{1}{7}={\tan }^{-1}\frac{2\cdot \frac{1}{3}}{1-\frac{1}{9}}+{\tan }^{-1}\frac{1}{7}\\ & ={\tan }^{-1}\frac{3}{4}+{\tan }^{-1}\frac{1}{7}={\tan }^{-1}\frac{\frac{3}{4}+\frac{1}{7}}{1-\frac{3}{4}\cdot \frac{1}{7}}\\ & ={\tan }^{-1}\frac{25}{25}={\tan }^{-1}1=45^{\circ }=\frac{\pi }{4}\end{array}$