2 cos*2 x-3sin x -3=0

$2cos^{2} x-3sinx-3=0 \\ 2(1-sin ^{2} x)-3sinx-3=0 \\ 2-2sin^{2} x-3sinx-3=0 \\ -2sin^{2} x-3sinx-1=0/*(-1)\\2sin^{2} x+3sinx+1=0 \\ sinx=t \\ 2t^{2} +3t+1=0 \\ D=9-8=1 \\ \sqrt{D} =1 \\ t _{1} = \frac{-3+1}{4} = \frac{-2}{4} =- \frac{1}{2} \\ t _{2} = \frac{-3-1}{4} =- \frac{4}{4} =-1 \\ sinx=- \frac{1}{2} \\ x=(-1) ^{n+1} \frac{ \pi }{6} + \pi n \\$

$sinx=-1 \\ x=- \frac{ \pi }{2} +2 \pi m$

n∈Z
m∈Z