Find the principal value of the following : cot(tan^-1 x + cot^-1 x)

Question

Find the principal value of the following :

\(\cot(\tan^{-1}\mathrm x + \cot^{-1}\mathrm x)\)

Answer 1

\(\cot(\tan^{-1}\mathrm x + \cot^{-1}\mathrm x)=\cot \left(\frac{\pi}{2}\right)\)

[ Formula: tan^-1 x + cot ^-1 x = \(\frac{\pi}{2}\)]

Putting value of cot\(\left(\frac{\pi}{2}\right)\)

=0