Помогите!!! sin7x+cos7x=корень из 2на sin11x

Решите задачу:

$\sin7x+\cos7x=\sqrt2\cos11x\\ \sin7x+\cos7x=\sqrt2(\frac{\sqrt2}{2}\sin7x+\frac{\sqrt2}{2}\cos7x)=\\=\sqrt2(\sin7x\cos\frac{\pi}{4}+\cos7x\sin\frac{\pi}{4})=\sqrt2\sin(7x+\frac{\pi}{4})\\\sin(7x+\frac{\pi}{4})=\cos11x\\\cos(\frac{\pi}{2}-(7x+\frac{\pi}{4}))=\cos11x\\\cos(\frac{\pi}{4}-7x)=\cos11x\\\frac{\pi}{4}-7x=\pm11x+2\pi k\\1)\frac{\pi}{4}-7x=11x+2\pi k\\18x=\frac{\pi}{4}-2\pi k\\x=\frac{\pi}{72}-\frac{\pi}{9}k\\2)\frac{\pi}{4}-7x=-11x+2\pi k\\4x=-\frac{\pi}{4}+2\pi k\\x=-\frac{\pi}{16}+\frac{\pi}{2}k$