Question

sin x - sin 2x + sin 3x - sin 4x = 0

Answer 1

$sin(x)-sin(2x)+sin(3x)-sin(4x)=0\sin(x)-sun(4x)+sin(3x)-sin(2x)=0\-2cos( frac{5x}{2} )sin(frac{3x}{2})+2cos(frac{5x}{2})sin(frac{x}{2})=0\-2cos(frac{5x}{2})(sin(frac{3x}{2})-sin(frac{x}{2}))=0\cos(frac{5x}{2})=0\frac{5x}{2}=frac{pi}{2}+pi k\x=frac{pi}{5}+frac{2pi k}{5}\sin(frac{3x}{2})-sin(frac{x}{2})=0\2cos( frac{frac{3x}{2}+frac{x}{2}}{2} )sin(frac{frac{3x}{2}-frac{x}{2}}{2})=2cos(frac{2x}{2})sin(frac{x}{2})=2cos(x)sin(frac{x}{2})\cos(x)=0\x=frac{pi}{2}+pik\sin(frac{x}{2})=0\x=2pik$
k∈Z
Ответ:$x=frac{pi}{5}+frac{2pi k}{5}\x=frac{pi k }{2}$