Question

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

Answer 1

`8/5`

Explanation:

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`