Question

Please answer my question sinx+sin2x+sin3x=cosx+cos2x+cos3x

Answer 1

1+sinx-sin2x=cosx+cos2x-cos3x
move cosx and cos3x to the left side
1+sinx-sin2x+cos3x-cosx=cos2x
cos3x-cosx=-2sin2x*sinx and cos2x=cos^2x-sin^2x and 1=sin^2x+cos^2x
subtract 1 from both sides
sinx-sin2x-2sin2x*sinx=cos^2x-sin^2x-(sin^2x+cos^2x)=>cos^2x-sin^2x-sin^2x-cos^2x
sinx-sin2x-2sin2x*sinx=-2sin^2x
add -2sin^2x for both sides
2sin^2x+sinx-sin2x-2sin2x*sinx=0
sin2x=2sinxcosx
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hello,
sinx*(2sinx+1-2cosx-2sin2x)=0 if sinx=0 x=k*pi
or 2(sinx-cosx-sin2x)+1=0