Question

Решить уравнение: cos(3x+pi/6)=cosx

Answer 1

$\cos(3x+\frac{\pi}{6}) = \cos x\\ \cos(3x+\frac{\pi}{6}) - \cos x=0\\ -2\sin(2x+\frac{\pi}{12})\sin(x+\frac{\pi}{12})=0\\\\ \sin(2x+\frac{\pi}{12}) = 0\\ 2x+\frac{\pi}{12} = \pi n\\ 2x = -\frac{\pi}{12} + \pi n\\ x = -\frac{\pi}{24} + \frac{\pi n}{2}\\\\ \sin(x+\frac{\pi}{12})=0\\ x+\frac{\pi}{12}=\pi n\\ x = -\frac{\pi}{12} + \pi n\\$