The value of $2 an ^{-1} \frac{1}{2}+ an ^{-1} \frac{1}{7}$

Question

The value of $2 	an ^{-1} \frac{1}{2}+	an ^{-1} \frac{1}{7}$

Aicharya · Accepted Answer

$\begin{aligned} & 2 	an ^{-1} \frac{1}{2}+	an ^{-1} \frac{1}{7} \ & =	an ^{-1}\left(\frac{2\left(\frac{1}{2}ight)}{1-\left(\frac{1}{2}ight)^2}ight)+	an ^{-1}\left(\frac{1}{7}ight) \ & =	an ^{-1}\left(\frac{4}{3}ight)+	an ^{-1}\left(\frac{1}{7}ight) \ & =	an ^{-1}\left(\frac{\frac{4}{3}+\frac{1}{7}}{1-\left(\frac{4}{3}ight)\left(\frac{1}{7}ight)}ight) \ & =	an ^{-1}\left(\frac{31}{17}ight)\end{aligned}$

The value of $2 \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{7}$

Solution