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Find the value of \[ \cot \;( \tan^{-1}a + \cot^{-1}a) \]

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  • \( tan^{-1}x+cot^{-1}x=\frac{\pi}{2}\) for all real x
  • cot\(\frac{\pi}{2}=0\)
Substituting, \( tan^{-1}x+cot^{-1}x=\frac{\pi}{2}\), $cot ( tan^{-1}a + cot^{-1}a) = cot \frac{\pi}{2}$.
We know that cot\(\frac{\pi}{2}=0\), hence $cot ( tan^{-1}a + cot^{-1}a) = 0$.
answered Feb 22, 2013 by thanvigandhi_1
edited Mar 14, 2013 by balaji.thirumalai
 

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