Question

Решите плз: ctg^2(2x)=1

Answer 1

$Ctg^{2}2x=1\\\\ 1)Ctg2x=1\\\\2x=arcCtg1+\pi n,n\in Z\\\\2x=\frac{\pi }{4}+\pi n,n\in Z\\\\x=\frac{\pi }{8}+\frac{\pi n }{2},n\in Z\\\\2)Ctg2x=-1\\\\2x=arcCtg(-1)+\pi n,n\in Z\\\\2x=\frac{3\pi }{4}+\pi n,n\in Z\\\\x=\frac{3\pi }{8}+\frac{\pi n }{2},n\in Z$