Question

Помогите с решением, пожалуйста

Answer 1

2 cos²8x + sin 6x = 1
1 + cos 16x + sin 6x = 1
cos 16x + sin 6x = 0
sin (π/2 - 16x) + sin 6x = 0
2·sin (π/4 - 5x)·cos (π/4 - 11x) = 0
$\left[\begin{array}{cc}sin( \frac{ \pi }{4}-5x) =0\\cos( \frac{ \pi }{4}-11x) =0\end{array}$
$\left[\begin{array}{cc}\frac{ \pi }{4}-5x = \pi n,nEZ\\\frac{ \pi }{4}-11x = \frac{ \pi}{2}+ \pi k,kEZ\end{array}$
$\left[\begin{array}{cc}5x =\frac{ \pi }{4}+ \pi n,nEZ\\\ 11x =-\frac{ \pi}{4}+ \pi k,kEZ\end{array}$
$\left[\begin{array}{cc}x =\frac{ \pi }{20}+\frac{ \pi n}{5} ,nEZ\\\ x =-\frac{ \pi}{44}+\frac{ \pi k}{11},kEZ\end{array}$