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