Question

Решите Уравнение : sin(11x)=sin(4x)

Answer 1

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

Answer 2

$sin11x=sin4x \ sin11x-sin4x=sin frac{11x-4x}{2}cos frac{11x+4x}{2}=sin frac{7x}{2}cos frac{15x}{2}=0 \ sin frac{7x}{2}=0 Rightarrow frac{7x}{2}=kpi Rightarrow x= frac{2}{7}kpi;kin Z \ cos frac{15x}{2}=0 Rightarrow frac{15x}{2}= frac{pi}{2}+npi Rightarrow x= frac{pi}{15}+ frac{2pi}{15}n; nin Z$