Question

Помогите решить задание 13 из ЕГЭ по математике!

Answer 1

$cos(2x)-sqrt{2}sin(x)+1=0\1-2sin^2(x)-sqrt{2}sin(x)+1=0\-2sin^2(x)-sqrt{2}sin(x)+2=0\2sin^2(x)+sqrt{2}sin(x)-2=0\D_{sin(x)}=2+4*2*2=18\sin(x)=frac{-sqrt{2}pmsqrt{18}}{4}=frac{-sqrt{2}pm3sqrt{2}}{4}=frac{sqrt{2}}{2};-sqrt{2}\sin(x)=-sqrt{2}\xinvarnothing\sin(x)=frac{sqrt{2}}{2}\x=frac{pi}{4}+2pi k, k in mathbb Z\x=frac{3pi}{4}+2pi k, k in mathbb Z$