Question

решите уравнение плииз​

Answer 1

$1)Ctg(\frac{\pi }{5}-x)+1=0\\\\Ctg(\frac{\pi }{5}-x)=-1\\\\\frac{\pi }{5}-x=\frac{3\pi }{4}+\pi n,n\in z\\\\-x=\frac{3\pi }{4}-\frac{\pi }{5}+\pi n,n\in z\\\\-x=\frac{11\pi }{20}+\pi n,n\in z\\\\x=-\frac{11\pi }{20}+\pi n,n\in z$

$2)Sin(3x-\frac{\pi }{4})Cos(3x-\frac{\pi }{4})=-\frac{1}{2}\\\\\frac{1}{2}*(2Sin(3x-\frac{\pi }{4})Cos(3x-\frac{\pi }{4}))=-\frac{1}{2} \\\\\frac{1}{2}Sin(6x-\frac{\pi }{2})=-\frac{1}{2}\\\\Sin(6x-\frac{\pi }{2})=-1\\\\Sin(\frac{\pi }{2}-6x)=1\\\\Cos6x=1\\\\6x=2\pi n,n\in z\\\\x=\frac{\pi n }{3} ,n\in z$