數學題 (eng)

a)
2sin²x - 3cosx = 0
2(1 - cos²x) - 3cosx = 0
2 - 2cos²x - 3cosx = 0
2cos²x + 3cosx - 2 = 0
(2cosx-1)(cosx+2) = 0
2cosx=1 or cosx+2=0(rej)
cosx = 1/2
x = 60, 300

b)
I use x instead of t because of good looking
2tanx = sec²x
2sinx/cosx = 1/cos²x
2sinxcos²x = cosx
2sinxcos²x - cosx = 0
cosx(2sinxcosx - 1) = 0
cosx=0 or 2sinxcosx-1=0
cosx=0 or sin2x=1
x=90, 270 or 2x=90, 450
x=90, 270 or x=45, 225

c)
cosx - sinx = 1
(cosx-sinx)² = 1²
cos²x - 2cosxsinx + sin²x = 1
1 - 2sinxcosx = 1
2sinxcosx = 0
sin2x = 0
2x = 0, 180, 360, 540, 720
x = 0, 90, 180, 270, 360

d)
sin2x - sinx = 0
2sinxcosx - sinx = 0
sinx(2cosx-1) = 0
sinx=0 or 2cosx-1=0
x=0, 180, 360 or cosx=1/2
x=0, 180, 360 or x=60, 300

應以 π 表示