Question

умоляю 1)Cos 5x-cos 7x+sin x=0​

Answer 1

$\displaystyle cos5x-cos7x+sinx=0\\\\-2sin(\frac{5x-7x}{2})*sin(\frac{5x+7x}{2})+sinx=0\\\\-2sin(-x)*sin6x+sinx=0\\\\2sinx*sin6x+sinx=0\\\\sinx(2sin6x+1)=0\\\\sinx=0; 2sin6x+1=0 \\\\sinx=0; x=\pi n; n \in Z\\\\sin6x=-\frac{1}{2}\\\\6x=-\frac{\pi }{6}+2\pi n; 6x=\frac{-5\pi }{6}+2\pi n\\\\x=-\frac{\pi }{36}+\frac{\pi n}{3}; x=\frac{-5\pi }{36}+\frac{\pi n}{3}; n \in Z$