Решите уравнение cos 2x+3sinx+1=0

Решите задачу:

$cos\ 2x+3sin\ x+1=0\\ cos^2x-sin^2x+3sin\ x+1=0\\ 1-sin^2x-sin^2x+3sin\ x+1=0\\ 2sin^2x-3sin\ x-2=0\\ D=9+16=25\\ sin\ x_1_,_2= \frac{3\pm 5}{4}=2;\ - \frac{1}{2}\\ sin\ x\neq 2,\ _T_. _K_. 2\notin[-1;\ 1]\\ sin\ x=- \frac{1}{2}\\ x= \frac{7\pi}{6}+2\pi n,\ n\in Z\\ x= \frac{11\pi}{6}+2\pi n,\ n\in Z\\\\ OTBET:\ x= \left \{ {{\frac{7\pi}{6}+2\pi n} \atop {\frac{11\pi}{6}+2\pi n}} \right. ,\ n\in Z$