Question

cos9x-cos7x+cos3x-cosx=0

Answer 1

$cos9x-cos7x+cos3x-cosx=0 \(cos9x-cos7x)+(cos3x-cosx)=0 \-2sin( frac{9x+7x}{2} )*sin( frac{9x-7x}{2} )-2sin( frac{3x+x}{2} )*sin( frac{3x+x}{2} )=0 \sin(8x)*sinx+sinx*sin(2x)=0 \sinx(sin(8x)+sin(2x))=0 \sinx*2*sin( frac{8x+2x}{2})*cos( frac{8x-2x}{2} )=0 \sinx*sin(5x)*cos(3x)=0 \sinx=0 \x_1=pi n, n in Z \ sin(5x)=0 \x=pi n \x_2= frac{pi n}{5} , n in Z \cos(3x)=0 \3x= frac{pi}{2} +pi n \x_3= frac{pi}{6} + frac{pi n}{3} , n in Z$