Question

СРОЧНО!!!!!
$2sin {x}^{2} + 3 sqrt{2} cos( frac{3pi}{2} + x) + 2 = 0$
(​Там синус в квадрате, а не x)

Answer 1

$2sin^2x+3sqrt2, cos(frac{3pi}{2}+x)+2=0\\2sin^2x+3sqrt2, sinx+2=0\\t=sinx; ,; ; -1leq tleq 1; ; ,; ; 2t^2+3sqrt2t+2=0; ,\\D=9cdot 2-4cdot 2cdot 2=18-16=2\\t_{1}=frac{-3sqrt2-sqrt2}{4}=frac{-4sqrt2}{4}=-sqrt2approx -1,4<-1; ; ne; ; podxodit\\t_2=frac{-3sqrt2+sqrt2}{2}=frac{-2sqrt2}{4}=-frac{sqrt2}{2}\\sinx=-frac{sqrt2}{2}; ; Rightarrow ; ; x=(-1)^{n}cdot (-frac{pi }{4})+pi n; ,; nin Z\\underline {x=(-1)^{n+1}cdot frac{pi}{4}+pi n; ,; nin Z}$