Question

Решите пожалуйста
sin 5x + sin x =0

Answer 1

$sin(5x)+sin(x)=0\\ 2sin( \frac{6x}{2})cos(\frac{4x}{2})=0\\sin(3x)cos(2x)=0\\ \left \{ {{sin(3x)=0} \atop {cos(2x)=0}} \right. \left \{ {{3x=k\pi} \atop {2x=\frac{\pi}{2}+k\pi }} \right. \left \{ {{x=\frac{k\pi}{3} } \atop {x=\frac{\pi}{4}+\frac{k\pi}{2} }} \right.$
k∈Z везде

Answer 2

$sin(5x)+sin(x)=0 \\ \\ 2sin( \frac{5x+x}{2})cos( \frac{5x-x}{2})=0 \\ \\ 2sin(3x)cos(2x)=0(/2) \\ \\ sin(3x)cos(2x)=0 \\ \\ \\ \left \{ {{sin(3x)=0} \atop {cos(2x)=0}} \right. \\ \\ \left \{ {{x= \frac{k \pi }{3},k-Z } \atop {x= \frac{ \pi }{4}+ \frac{k \pi }{2} , k-Z}} \right.$


Ответ:$\left \{ {{x= \frac{k \pi }{3},k-Z } \atop {x= \frac{ \pi }{4}+ \frac{k \pi }{2} , k-Z}} \right.$