A.Maths(sums & products of trigonometric functions)

1. sin2x + sin3x = 0
2sin[(2x + 3x) / 2]cos[(2x - 3x) / 2] = 0
sin[5x / 2]cos[-x / 2] = 0
sin(5x / 2)cos(x / 2) = 0
sin(5x / 2) = 0 or cos(x / 2) = 0
5x / 2 = 0°, 180°, 360°, 540°, 720° or x / 2 = 90°.
x = 0°, 72°, 144°, 216°, 288° or x = 180°.
2. cosx + cos2x + cos3x = 0
cosx + cos3x + cos2x = 0
2cos[(x + 3x) / 2]cos[(x - 3x) / 2] + cos2x = 0
2cos2x cos(-x) + cos2x = 0
2cos2x cosx + cos2x = 0
cos2x(2cosx + 1) = 0
cos2x = 0 or cosx = -1 / 2
2x = 90°, 270°, 450°, 630° or x = 120°, 240°
x = 45°, 135°, 225°, 315° or 120°, 240°

sin2x+sin3x=0
2sin(5x/2)cos(-x/2)=0
sin(5x/2)=0 or cos(-x/2)=0
5x/2=0or180or360or540or720or900 or x/2=90or270or450or630 (degree)
x=0,72,144,216,288,360,45,135,225or315(degree)

i don't know whether the range of x is smaller than 360(degree) or smaller and equals x,
so i expected x can be equal to 360(degree)

cosx+cos2x+cos3x=0
cosx+cos3x+cos2x=0
2cos(2x)cos(-x)+cos2x=0
cos2x(2cosx+1)=0
cos2x=0 or 2cosx+1=0
2x=90or270or450or630 or cosx=-1/2
x=45or135or225or315(degree) or x=120or240(degree)

2006-11-05 20:46:20 補充：
sin2x sin3x=02sin(5x/2)cos(-x/2)=0sin(5x/2)=0 or cos(-x/2)=05x/2=0or180or360or540or720or900 or x/2=90(degree)x=0,72,144,216,288,360,180(degree)