Question

sin3x-sinx=0 решаем ребята)

Answer 1

$sin 3x-sin x=0\3sin x-4sin^3x-sinx=0\2sin x-4sin^3x=0\2sin x(1-2sin^2x)=0\sin x=0\x=pi n,ninmathbb{Z}\sin x=pmcfrac{1}{sqrt{2}}\sin x=cfrac{1}{sqrt{2}}\x=cfrac{pi}{4}+2pi n,ninmathbb{Z}\x=cfrac{3pi}{4}+2pi n,ninmathbb{Z}\sin x=-cfrac{1}{sqrt{2}}\x=cfrac{5pi}{4}+2pi n,ninmathbb{Z}\x=cfrac{7pi}{4}+2pi n,ninmathbb{Z}$