Evaluate $cot ({tan}^{- 1} a + {cot}^{- 1} a)$

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Solution

$cot ({tan}^{- 1} a + {cot}^{- 1} a)$
$= cot (\frac{π}{2} - {cot}^{- 1} + {cot}^{- 1} a)$

$= cot (\frac{π}{2})$
$= 0.$
Hence, the answer is $0.$

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