The value of $ an ^{-1}\left(\frac{1}{8} ight)+ an ^{-1}\left(\frac{1}{2} ight)+ an ^{-1}\left(\frac{1}{5} ight)$ is

Question

The value of $	an ^{-1}\left(\frac{1}{8}ight)+	an ^{-1}\left(\frac{1}{2}ight)+	an ^{-1}\left(\frac{1}{5}ight)$ is

Aicharya · Accepted Answer

$\begin{aligned} & 	an ^{-1}\left(\frac{1}{8}ight)+	an ^{-1}\left(\frac{1}{2}ight)+	an ^{-1}\left(\frac{1}{5}ight) \ & =	an ^{-1}\left(\frac{1}{8}ight)+	an ^{-1}\left(\frac{\frac{1}{2}+\frac{1}{5}}{1-\frac{1}{2} \cdot \frac{1}{5}}ight) \ & =	an ^{-1}\left(\frac{1}{8}ight)+	an ^{-1}\left(\frac{7}{9}ight) \ & =	an ^{-1}\left(\frac{\frac{1}{8}+\frac{7}{9}}{1-\frac{1}{8} \cdot \frac{7}{9}}ight) \ & =	an ^{-1}\left(\frac{\frac{72}{65}}{\frac{72}{9}}ight) \ & =	an ^{-1}(1) \ & =\frac{\pi}{4}\end{aligned}$

The value of $\tan ^{-1}\left(\frac{1}{8}\right)+\tan ^{-1}\left(\frac{1}{2}\right)+\tan…

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