sin5x+sinx+2sin^2x=1

Question

sin5x+sinx+2sin^2x=1

Answer 1

2cos2xcos3x=1-2sin^2x

 2cos2xcos3x=cos2x

cos2x(2cos3x-1)=0

cos2x=0 или cos3x = 1/2

2x=pi/2+pi*n

 

x=pi/4+pi*n/2

или

3x=+-pi/3+2pi*n

 

x=+-pi/9+2pi*n/3