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The value of $\cot^{-1}(-x)$ for all $x\;\in\;R$ in terms of $\cot^{-1}x$ is ____________.

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  • Principal interval of cot is \((0,\pi)\)
  • \(cot(\pi-\theta)=-cot\theta\)
\(Ans:\:\: \pi - cot^{-1}x\)
Since cot is -ve in the interval \((\frac{\pi}{2},\pi)\), the angle is to be reduced and brought within this interval.
Let \( x=cot\theta,\:\:\Rightarrow\:\theta=cot^{-1}x\)


answered Feb 18, 2013 by thanvigandhi_1
edited Mar 10, 2013 by rvidyagovindarajan_1
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