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

Toolbox:
• $tan^{-1}x+cot^{-1}x=\frac{\pi}{2}$ 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 $cot ( tan^{-1}a + cot^{-1}a) = 0$.
edited Mar 14, 2013