Решение: 2sin(5x)sin(2x)=cosx

Question

Решение: 2sin(5x)sin(2x)=cosx

Answer 1

Sina*sinb=1/2[cos(a-b)-cos(a+b)]
2sin5x*sin2x=cos(3x)-cos(7x)
cos3x-cos7x=cosx
cos3x=cos7x+cosx
cos3x=2cos3xcos4x
cos3x(1+2cos4x)=0
1. cos3x=0   3x=π/2+πn  x=π/6+πn/3    n∈Z
2.  1+2cos4x=0
      cos4x=-1/2
       4x=+-2π/3+2πn    x=+-π/6+πn/2   n∈Z