find the general solution of equation sinx-3sin2x+sin3x=cos x-3 cos 2X+cos3x

sinx-3sin2x+sin3x=cosx-3cos2x+cos3x

sinx+sin3x-3sin2x-cosx+cos3x+3cos2x=0

2sinx+3x2cosx-3x2-3sin2x-2cosx+3x2cosx-3x2+3cos2x=0

2sin2xcosx-3sin2x-2cos2xcosx+3cos2x=0

sin2x2cosx-3-cos2x2cosx-3=0

2cosx-3sin2x-cos2x=0

cosx=32, or, sin2x=cos2x

As, cos x[-1,1]. Thus,cos x32

So,

sin2x=cos2xtan2x=1tan2x=tanπ4

2x=nπ+π4

x=nπ2+π8

  • 138
What are you looking for?