Question

2√2*sin(x)+√2sinx*cosx-cosx-2=0

Answer 1

$2\sqrt2\cdot sina+\sqrt2sinx\cdot cosx-cosx-2=0\\\\\sqrt2sinx\cdot (2+cosx)-(cosx+2)=0\\\\(2+cosx)\cdot (\sqrt2sinx-1)=0\\\\a)\; \; 2+cosx=0\; \; \to \; \; \; cosx=-2<-1\; \; \Rightarrow \; \; \; x\in \varnothing \\\\b)\; \; \sqrt2sinx-1=0\; \; \to \; \; sinx=\frac{1}{\sqrt2}\; \; ,\; \; x=(-1)^{n}\cdot \frac{\pi }{4}+\pi n\; ,\; n\in Z\\\\Otvet:\; \; x=(-1)^{n}\cdot \frac{\pi }{4}+\pi n\; ,\; n\in Z\; .$