$\cot ({\tan ^{ - 1}}a + {\cot ^{ - 1}}a)$
$\cot ({\tan ^{ - 1}}a + {\cot ^{ - 1}}a)$
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$\cot ({\tan ^{ - 1}}a + {\cot ^{ - 1}}a) = \cot \left( {{{\tan }^{ - 1}}a + \frac{\pi }{2} - {{\tan }^{ - 1}}a} \right) = \cot \frac{\pi }{2} = 0$
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