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