Question

Решить уравнения
1) cosx-cos2x=0
2) sin5x-sinx=0

Answer 1

$1) \cos(x) - \cos(2x) = 0 \\ - 2 \sin( \frac{3x}{2} ) \sin( - \frac{x}{2} ) = 0 \\ \sin( \frac{3x}{2} ) \sin( \frac{x}{2} ) = 0 \\ \sin( \frac{x}{2} ) = 0 \\ x = \frac{2k\pi}{3} \\ 2) \sin(5x) - \sin(x) = 0 \\ 2 \cos(3x) \sin(2x) = 0 \\ \cos(3x) \sin(2x) = 0 \\ \\ \cos(3x) = 0 \\ \sin(2x) = 0 \\ \\x = \frac{\pi}{6} + \frac{k\pi}{3} \\ \frac{k\pi}{2}$