How do you evaluate $cot^-1(1)$ without a calculator?

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Answer 1 · 2016-08-18T04:14:06

$cot^-1(1)=pi/4$ .

Recall the Defn. of $cot^-1$ fun. :

$cot^-1x=theta, x in RR iff cottheta=x, theta in (0, pi)$ .

Since $cot(pi/4)=1, &, pi/4 in (0, pi),$ we have, $cot^-1(1)=pi/4$ .

How do you evaluate cot^-1(1)cot^-1(1) without a calculator?