✔ 最佳答案
1.
sin3x + cos3x = sinx + cosx
sin3x - sinx + cos3x - cosx = 0
2cos[(3x + x)/2]sin[(3x - x)/2] - 2sin[(3x + x)/2]sin[(3x - x)/2] = 0
2cos2xsinx - 2sin2xsinx = 0
-2sinx[sin2x - cos2x] = 0
sinx = 0 or sin2x = cos2x
sinx = 0 or tan2x = 1
x = 0o, 180o or 2x = 45o, 225o, 405o, 585o
x= 0o, 180o or x = 22.5o, 112.5o, 202.5o, 292.5o
2.
cosx + cos2x + cos3x = 0
(cos3x + cosx) + cos2x = 0
2cos[(3x + x)/2]cos[(3x - x)/2] + cos2x = 0
2cos2xcosx + cos2x = 0
cos2x(2cosx + 1) = 0
cos2x = 0 or cosx = -1/2
2x = 90o, 270o, 450o, 630o or x = 120o, 240o
x = 45o, 135o, 225o, 315o or x = 120o, 240o
3.
sinx + sin2x + sin3x + sin4x = 0
(sin3x + sinx) + (sin4x + sin2x) = 0
2sin[(3x + x)/2]cos[(3x - x)/2] + 2sin[(4x + 2x)/2]cos[(4x - 2x)/2] = 0
2sin2xcosx + 2sin3xcosx = 0
2cosx(sin2x + sin3x) = 0
2cosx•2sin[(2x + 3x)/2]cos[(3x - 2x)/2] = 0
4cosxsin(5x/2)cos(x/2) = 0
cosx = 0 or sin(5x/2) = 0 or cos(x/2) = 0
x = 90o, 270o or (5x/2) = 0o, 180o, 360o, 540o, 720o, 900o or (x/2) = 90o
x = 90o, 270o or x = 0o, 72o, 144o, 216o, 288o, 360o or x = 180o
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