Решить. за . 1)2sin (40°+x)sin(x-50°)+1=0 2)4cos^2x+sinxcosx+3sin^2x-3=0 3)cos^2x-3sinxsosx=-1

1
2sin (40°+x)sin(x-50°)+1=0
sin (40°+x)sin(x-50°)=-1/2
1/2*[cos(40+x-x+50)-cos(40+x+x-50)]=-1/2
cos90-cos(2x-10)=-1/2
cos(2x-10)=1/2
2x-10=-60+360k U 2x-10=60+360k
2x=-50+360k U 2x=70+360k
x=25+180k U x=35+180k,k∈z
2
4cos^2x+sinxcosx+3sin^2x-3=0
4cos²x+sinxcosx+3sin²x-3cos²x-3sin²x=0
cos²x+sinxcosx=0
cosx(cosx+sinx)=0
cosx=0⇒x=π/2+πk,k∈z
cosx+sinx=0/cosx
1+tgx=0
tgx=-1⇒x=-π/4+πk,k∈z
3
cos^2x-3sinxcosx=-1
cos²x-3sinxcosx+sin²x+cos²x=0 /cos²x
tg²x+3tgx+2=0
tgx=a
a²+3a+2=0
D=9-8=1>0
a1+a2=-3 U a1+a2=2
a1=-2⇒tgx=-2⇒x=-arctg2+πk,k∈z
a2=-1⇒tgx=-1⇒x=-π/4+πk,k∈z