Question

Решите уравнение на фото

Answer 1

$\sqrt{3}Cosx=Sin^{3}x+\sqrt{3}Cos^{3}x\\\\\sqrt{3}Cosx-\sqrt{3}Cos^{3}x=Sin^{3}x\\\\\sqrt{3}Cosx(1-Cos^{2}x)-Sin^{3}x=0\\\\\sqrt{3}Cosx*Sin^{2}x-Sin^{3}x=0\\\\Sin^{2} x(\sqrt{3} Cosx-Sinx)=0\\\\1)Sin^{2}x=0\\\\Sinx=0\\\\x=\pi n,n\in z\\\\2)\sqrt{3}Cosx-Sinx=0|:Cosx\neq0\\\\\sqrt{3}-tgx=0\\\\tgx=\sqrt{3}\\\\x=arctg\sqrt{3}+\pi n,n\in z\\\\x=\frac{\pi }{3}+\pi n,n\in z$

x = πn

Корни : 0 ; π ; 2π

$x=\frac{\pi }{3}+\pi n,n\in z$

Корни :

$\frac{\pi }{3};\frac{4\pi }{3};\frac{7\pi }{3}$