Question

49 ,решительно пример 1+cosx+√3cos x/2=0

Answer 1

$1+Cosx+\sqrt{3}Cos\frac{x}{2}=0\\\\2Cos^{2}\frac{x}{2}+\sqrt{3}Cos\frac{x}{2}=0\\\\Cos\frac{x}{2}(2Cos\frac{x}{2}+\sqrt{3})=0\\\\1)Cos\frac{x}{2}=0\\\\\frac{x}{2}=\frac{\pi }{2}+\pi n,n\in z\\\\x_{1} =\pi + 2\pi n,n\n z\\\\2)2Cos\frac{x}{2} +\sqrt{3}=0$

$2Cos\frac{x}{2}=-\sqrt{3}\\\\Cos\frac{x}{2}=-\frac{\sqrt{3} }{2} \\\\\frac{x}{2}=\pm arcCos(-\frac{\sqrt{3} }{2})+2\pi n,n\n z\\\\\frac{x}{2} =\pm (\pi -arcCos\frac{\sqrt{3} }{2})+2\pi n,n\in z\\\\\frac{x}{2}=\pm (\pi-\frac{\pi }{6})+2\pi n,n\n z\\\\\frac{x}{2}=\pm \frac{5\pi }{6}+2\pi n,n\n z\\\\x_{2}=\pm \frac{5\pi }{3}+4\pi n,n\in z$

Answer 2

Решение приложено

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