решить уравнение sin 5x+sin x +2(sin квадрат) x=1

Question

решить уравнение sin 5x+sin x +2(sin квадрат) x=1

Answer 1

sin5x+sinx=1-2sin^2x                                             1-sin^2x-sin^2x=cos^2x-sin^2x=cos2x

                                                                          sinx+siny=2sin(x+y)/2cos(x-y)/2

2sin3xcos2x-cos2x=0

cos2x(2sin3x-1)=0

1)cos2x=0                          2)2sin3x-1=0

   2x=п/2+2пn                        2sin3x=1

    x=п/4+пn                          sin3x=1/2

                                             3x=п/6+пn

                                               x=п/18+пn/3