7
1-2sin²x+sinx=0
sinx=a
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-1/2⇒sinx=-1/2⇒x=(-1)^(n+1)*π/6+πn,n∈z
a2=(1+3)/4=1⇒sinx=1⇒x=π/2+2πk,k∈z
8
sin²a-2sina*sinb+sin²b+cos²a-2cosa*cosb+bos²b=
=(sin²a+cos²a)+(sin²b+cos²b-2(cosa*cosb+sina*sinb)=
=2-2cos(a-b)=2(1-cos(a-b))
4sin²(a-b)/2=4*(1-cos(a-b))/2=2(1-cos(a-b))
2(1-cos(a-b))=2(1-cos(a-b))