Question

Решить уравнение. раскрыла косинус и синус по формулам, подскажите, что дальше делать

Answer 1

$\frac{2}{1-Cos(2x+\frac{\pi }{3})}=Sin(x+\frac{\pi }{6})\\\\\frac{2}{2Sin^{2} (x+\frac{\pi }{6})}-Sin(x+\frac{\pi }{6})=0\\\\\frac{1}{Sin^{2}(x+\frac{\pi }{6})}-Sin(x+\frac{\pi }{6} )=0\\\\\frac{1-Sin^{3}(x+\frac{\pi }{6})}{Sin^{2}(x+\frac{\pi }{6})}=0\\\\Sin(x+\frac{\pi }{6})\neq 0\\\\1-Sin^{3}(x+\frac{\pi }{6})=0\\\\Sin^{3}(x+\frac{\pi }{6}) =1$

$Sin(x+\frac{\pi }{6})=1\\\\x+\frac{\pi }{6}=\frac{\pi }{2}+2\pi n,n\in z\\\\x=\frac{\pi }{2}-\frac{\pi }{6} +2\pi n,n\in z\\\\x=\frac{\pi }{3}+2\pi n,n\in z$