Question

Write the value of  \[\tan^{- 1} \left( \frac{1}{x} \right)\]  for x < 0 in terms of `cot^-1x`

Answer 1

\[\tan^{- 1} \left( \frac{1}{x} \right) = \tan^{- 1} \left( - \frac{1}{x} \right)\text{ for } x < 0\]
\[ = - \tan^{- 1} \left( \frac{1}{x} \right)\]
\[ = - \cot^{- 1} x\]
\[ = - \left( \pi - \cot^{- 1} x \right)\]
\[ = - \pi + \cot^{- 1} x\]