Question

Which value is a solution for the equation cot(x/2)=1?

pi/4
3pi/4
7pi/4
5pi/2

Answer 1

cot(x/2)=1 cot^(-1) both sides
x/2=pi/4
x= pi/2
since it is cot and thus osculating, we can say:
\[x=\frac{n\pi}{2} : n\in\mathbb{Z}\]
so 5pi/2 is a solution.