Решите Уравнение : sin(11x)=sin(4x)

sin11x-sin4x=0 2sin(7x/2)cos(15x/2)=0 sin(7x/2)=0⇒7x/2=πn⇒x=2πn/7,n∈Z cos(15x/2)=0⇒15x/2=π/2+πn⇒x=π/15+2πn/15,n∈Z

[latex]sin11x=sin4x \\ sin11x-sin4x=sin \frac{11x-4x}{2}cos \frac{11x+4x}{2}=sin \frac{7x}{2}cos \frac{15x}{2}=0 \\ sin \frac{7x}{2}=0 \Rightarrow \frac{7x}{2}=k\pi \Rightarrow x= \frac{2}{7}k\pi;k\in Z \\ cos \frac{15x}{2}=0 \Rightarrow \frac{15x}{2}= \frac{\pi}{2}+n\pi \Rightarrow x= \frac{\pi}{15}+ \frac{2\pi}{15}n; n\in Z \\ [/latex]