Answer:
[tex] x = {\sin^{ - 1} 2} \: \: or \: \: x = \frac{7\pi}{6}, \: \: \frac{5\pi}{3} [/tex]
Step-by-step explanation:
[tex]2 { \cos}^{2} x + 3 \sin x = 0 \\ 2 {(1 - \sin}^{2} x) + 3 \sin x = 0 \\ 2 - 2 \sin^{2} x+ 3 \sin x = 0 \\ 2 \sin^{2} x - 3 \sin x - 2 = 0 \\ 2 \sin^{2} x - 4\sin x + \sin x- 2 = 0 \\ 2\sin x(\sin x - 2) + 1(\sin x - 2) = 0 \\ (\sin x - 2)(2\sin x + 1) = 0 \\ (\sin x - 2) = 0 \: or \: (2\sin x + 1) = 0 \\ \sin x = 2 \: or \: 2\sin x = - 1 \\ x = {\sin^{ - 1} 2} \: \: or \: \: \sin x = - \frac{1}{2} \\ x = {\sin^{ - 1} 2} \: \: or \: \: x = \frac{7\pi}{6}, \: \: \frac{5\pi}{3} [/tex]
