sin5x+sinx+2sin^2x=1
2sin3xcos2x + 2sin^2x - cos^2x - sin^2x = 0
2sin3xcos2x + sin^2x - cos^2x = 0 | * (-1)
-2sin3xcos2x +cos^2x - sin^2x = 0
-2sin3xcos2x + cos2x = 0 | *(-1)
2sin3xcos2x - cos2x = 0
cos2x( 2sin3x-1) = 0
cos2x = 0 или 2sin3x -1 = 0
2x = п/2 + пк, к ∈ z
x = п/4 + пк/2, к ∈ z
sin3x = 1/2
3x = (-1)^n п/6 + пn, n ∈ z
x= (-1)^n п/18 + пn/3, n ∈ z