Question

Solve 2cos^2x+3sinx=0

Answer 1

`x = {\sin^( - 1) 2} \: \: or \: \: x = (7\pi)/(6), \: \: (5\pi)/(3)`

Explanation:

`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 = - (1)/(2) \\ x = {\sin^( - 1) 2} \: \: or \: \: x = (7\pi)/(6), \: \: (5\pi)/(3)`