Question

Решить уравнения: 1) sin2x*cosx=cos2x*sinx 2) √3sin2x + cos 5x - cos9x = 0 3) sinx*cos2x + cosx*cos4x = sin(п/4 + 2x)*sin(п/4 - 3х)

Answer 1

$1) sin(2x)cos(x)=cos(2x)sin(x) = sin(2x-x) = sin(x) \\ sin(x) = 0 \\ x = \pi n, n \to Z \\ \\ 2) \sqrt{3} sin(2x) + cos(5x) - cos(9x) = 0 \\ sin(7x) = - \frac{ \sqrt{3} }{2} \\ 7x= (-1)^{n+1} \frac{ \pi}{3} + \pi n, n \to Z \\ x = (-1)^{n+1} \frac{ \pi}{21} + \frac{ \pi n}{7}, n \to Z$