Question

решите уравнение:
$2(sinx+cosx)+1+sin2x=0$

Answer 1

$2(sinx+cosx)+1+sin2x=0\\t=sinx+cosx; ; to \\ t^2=sin^2x+2sinxcdot cosx+cos^2x=1+sin2x; to ; ; sin2x=t^2-1\\\2t+1+(t^2-1)=0\\t^2+2t=0\\t(2+t)=0; ; Rightarrow quad t_1=0; ,; ; t_2=-2\\a); ; sinx+cosx=0; |:cosxne 0\\tgx+1=0\\tgx=-1\\x=-frac{pi}{4}+pi n,; nin Z$

$b); ; sinx+cosx=-2; |:sqrt2\\frac{1}{sqrt2}=frac{sqrt2}{2}\\frac{sqrt2}{2}sinx+ frac{sqrt2}{2}cosx=-frac{2}{sqrt2}$

$cos frac{pi}{4}cdot sinx+sinfrac{pi}{4}cdot cosx=-sqrt2; ,; ; -sqrt2approx -1,41\\sin(x+frac{pi}{4})=-sqrt2 textless -1; ; ; ; net; reshenij,; t.k.; -1 leq sin alpha leq 1\\Otvet:; ; x=-frac{pi}{4}+pi n,; nin Z; .$

Answer 2

https://znanija.com/task/24524022

Answer 3

https://znanija.com/task/24524166

Answer 4

https://znanija.com/task/24524146