F.4 A.Maths Trigo Question

1
sinx - sin3x = cosx - cos3x

sin3x - sinx = cos3x - cosx

2cos[(3x + x)/2]sin[(3x - x)/2] = -2sin[(3x + x)/2]sin[(3x - x)/2]

cos2xsinx = -sin2xsinx

sinx(cos2x + sin2x) = 0

sinx = 0 or cos2x + sin2x = 0

sinx = 0 or tan2x = -1

x = 0ﾟ, 180ﾟ or 360ﾟ,

or 2x = 135ﾟ, 315ﾟ, 495ﾟ or 675ﾟ

x = 0ﾟ, 67.5ﾟ, 157.5ﾟ, 180ﾟ, 247.5ﾟ, 337.5ﾟ or 360ﾟ
2

sinx+sin3x+sin5x=0
(sinx+sin5x)+sin3x=0
2sin[(5x+x)/2]cos[(5x-x)/2]+sin3x=0
2sin3xcos2x+sin3x=0
sin3x(2cos2x+1)=0
sin3x=0 or cos2x=-1/2
3x=0,180,360,540,720,900,1080 or 2x=120,240,480,600
x=0,60,120,180,240,300,360 or x=60,120,240,300
x=0,60,120,180,240,300,360