Question

tgπ(x-4)/2=1
Решить уравнение

Answer 1

$tg(\frac{\pi(x-4)}2)=1\\\\\frac{\pi(x-4)}2=\frac{\pi}4+\pi n;n\in Z\\\\\pi(x-4)=\frac{\pi}2+2\pi n;n\in Z\\\\x-4=\frac{1}2+2n;n\in Z\\\\x=\frac{1}2+4+2n;n\in Z\\\\x=\frac{1}2+\frac{8}2+2n;\in Z\\\\x=\frac{9}2+2n;n\in Z\\\\x=4.5+2n;n\in Z$