[latex]2cos^2x+sinx+1=0[/latex]

cos^2 x = 1 - sin^2 x  2cos^2 x - sin x - 1 = 0  2(1 - sin^2 x) - sin x - 1 = 0  2sin^2 x + sin x - 1 = 0 

[latex]2cos^2x+sinx+1=0 \\ 2*(1-sin^2x)+sinx+1=0 \\ 2-2sin^2x+sinx+1=0 \\ -2sin^2x+sinx+3=0 \\ \\ y=sinx \\ \\ -2y^2+y+3=0 \\ D=b^2-4ac=1^2-4*(-2)*3=1+24=25 \\ y_1_,_2= \frac{-b_-^+ \sqrt{D} }{2a} \\ \\ y_1= \frac{-1- \sqrt{25} }{2*(-2)}= \frac{-1-5}{-4}= \frac{-6}{-4}= \frac{3}{2} \\ \\ y_2= \frac{-1+ \sqrt{25} }{2*(-2)}= \frac{-1+5}{-4}= \frac{4}{-4}=-1 \\ \\ sinx_1= \frac{3}{2} \\ x_1=0,0261 \\ \\ sinx_2=-1 \\ x_2= \frac{3 \pi }{2} [/latex]