Question

Помогите отдам 25 баллов!!!!

Answer 1

$1)tg(2x-\frac{\pi }{4})=-1 \\\\2x-\frac{\pi }{4}=arctg(-1)+\pi n,n\in Z\\\\2x-\frac{\pi }{4}=-\frac{\pi }{4}+\pi n,n\in Z\\\\2x=-\frac{\pi }{4}+\frac{\pi }{4} +\pi n,n\in Z\\\\2x=\pi n,n\in Z\\\\x=\frac{\pi n }{2},n\in Z\\\\2)x\in[-\frac{\pi }{4};\frac{\pi }{4}] \\\\n=-1\Rightarrow x=-\frac{\pi }{2}\notin[-\frac{\pi }{4};\frac{\pi }{4}]\\\\n=0\Rightarrow x=0\in[-\frac{\pi }{4},\frac{\pi }{4}]\\\\n=1\Rightarrow x=\frac{\pi }{2} \notin[-\frac{\pi }{4} ;\frac{\pi }{4}]$

$Otvet:\boxed{1)x=\frac{\pi n }{2},n\in Z; \ 2)x=0}$