Question

ешите уравнение
Sin5x+sinx=0

Answer 1

$sin5x+sinx=0\ 2sinfrac{5x+x}{2}cosfrac{5x-x}{2}=0\2sin3xcos2x=0\ sin3xcos2x=0\ sin3x=0; 3x=pi n;x=frac{pi n}{3} =frac{pi}{3}n \ cos2x=0; 2x=frac{pi}{2}+pi k;x=frac{pi}{4}+frac{pi k}{2}=frac{pi}{4} +frac{pi}{2} k$

Answer 2

$sin5x+sinx=0 \ 2sin frac{5x+x}{2} cos frac{5x-x}{2} =0 \ 2sin3xcos2x=0 \ 2sin3x=0 \ sin3x=0 \ 3x= pi n \ x= frac{ pi n}{3} \ cos2x=0 \ 2x= frac{ pi }{2} + pi n \ x= frac{ pi }{4} + frac{ pi n}{2}$
n∈Z