sinx+cosx=t
(sinx+cosx)^2=t^2 ⇒ sin^2x+2sinx*cosx+cos^2x=t^2 ⇒ 1+2sinx*cosx=t^2
3*(t^2-1)>t+1
3t^2-t-4 >0
D=1-4*3*(-4)=49
t_(1)=-1; t_(2)=4/3
t <-1 ИЛИ t > 4/3
sinx+cosx <-1
cosx=sin((π/2)-x)
sinx+cosx=sinx+sin((π/2)-x)=2sin(π/4)cos(x-(π/4))=2*(sqrt(2)/2)cos(x-(π/4))=sqrt(2)cos(x-(π/4))
sqrt(2)cos(x-(π/4)) < -1
cos(x-(π/4)) <-1/sqrt(2)
(3π/4)+2πn < x-(π/4) < (5π/4)+2πn
[b](π)+2πn < x < (3π/2)+2πn [/b]
ИЛИ
sqrt(2)cos(x-(π/4)) <4/3
cos(x-(π/4)) >2sqrt(2)/3
-arccos(2sqrt(2)/3)+2πn < x-(π/4) < arccos(2sqrt(2)/3)+2πn
[b](π/4)-arccos(2sqrt(2)/3)+2πn < x < arccos(2sqrt(2)/3)+(π/4)+2πn [/b]
n ∈ Z