Question

решите уравнение 2cos^2x +(2- √2)sinx+√2-2=0

Answer 1

$2cos^2x +(2- sqrt{2} )sin x+ sqrt{2} -2=0$
$2-2sin^2x +(2- sqrt{2} )sin x+ sqrt{2} -2=0$
$-2sin^2x +(2- sqrt{2} )sin x+ sqrt{2} =0$
$2sin^2x -( 2-sqrt{2} )sin x- sqrt{2} =0$
$2sin^2x - 2sin x+sqrt{2} sin x- sqrt{2} =0$
$2sin x(sin x - 1)+sqrt{2} (sin x-1)=0$
$(sin x - 1)(2sin x+sqrt{2})=0$
$left[begin{array}{l} sin x - 1=0 \ 2sin x+sqrt{2}=0 end{array}$
$left[begin{array}{l} sin x = 1 \ sin x=- frac{ sqrt{2} }{2} end{array}$
$left[begin{array}{l} x_1 = frac{ pi }{2}+2 pi n, nin Z \ x_2=(-1)^{k+1} frac{ pi }{4}+ pi k, kin Z end{array}$