Sinx+cosx=a
(sinx+cosx)²=a²
sin²x+2sinxcosx+cos²x=a²
1+sin2x=a²
sin2x=a²-1
a²-1=3(a-1)
a²-1-3a+3=0
a²-3a+2=0
a1+a2=3 U a1*a2=2
a1=1 U a2=2
1)sinx+cosx=1
√2*(√2/2*sinx+√2/2*cosx)=1
√2sin(x+π/4)=1
sin(x+π/4)=1/√2
x+π/4=π/4+2πn U x+π/4=3π/4+2πn
x=-π/4+π/4+2πn U x=3π/4-π/4+2πn
x=2πn,n∈z U x=π/2+2πn,n∈z
2)√2sin(x+π/4)=2
sin(x+π/4)=√2>1 нет решения