sin²x+cos²x+2sin x*cos x=cjs x+sin x
(sin x+cos x)²-(cos x+sin x)=0
sin x+cos x) (sin x+cos x-1)=0
1)sin x+cos x=0 /cos x
tg x=-1 x=-π/4=πn n∈z
2)sin x+cos x=1 sin x+sin(π/2-x)=1 2sin(x+π/2-x)/2cos (x-π/2+x)/2=1
2sinπ/4*cos(x-π/4)=1 2*√2/2*cos(x-π/4)=1 √2cos(x-π/4)=1 cos (x-π/4)=√2/2
x-π/4= +-π/4+2πn x=+-π/4+π/4+2πn
x1=π/4+π/4+2πn=π/2+2πn. n∈z
x2=-π/4+π/4+2πk=2πk. k∈z