Question

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

Answer 1

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