Question

${\tan }^{-1}\frac{1}{3}+{\tan }^{-1}\frac{1}{5}+{\tan }^{-1}\frac{1}{7}+{\tan }^{-1}\frac{1}{8}=$

• A. $\pi$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\frac{3\pi }{4}$

Answer 1

Answer: (B)

Given expression is equal to
${\tan }^{-1}\left(\frac{\frac{1}{3}+\frac{1}{5}}{1-\frac{1}{15}}\right)+{\tan }^{-1}\left(\frac{\frac{1}{7}+\frac{1}{8}}{1-\frac{1}{56}}\right)$
$={\tan }^{-1}\frac{4}{7}+{\tan }^{-1}\frac{3}{11}={\tan }^{-1}\left(\frac{\frac{4}{7}+\frac{3}{11}}{1-\frac{12}{77}}\right)=\frac{\pi }{4}$