How do you find the exact value of $cot (arctan (5/8))$ ?

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Answer 1 · 2016-03-24T15:10:12

$8/5$

Recall that $cot(x)=1/tan(x)$ . Thus,

$cot(arctan(5/8))=1/tan(arctan(5/8))$

$tan(x)$ ard $arctan(x)$ are inverse functions, so $tan(arctan(x))=x$ and $tan(arctan(5/8))=5/8$ .

So, we obtain:

$1/tan(arctan(5/8))=1/(5/8)=8/5$

How do you find the exact value of cot (arctan (5/8))cot (arctan (5/8))?