1.已知 向量m=(2sinB,-√3),向量n=(cos2B,-2cos^2(B/2).
∵ 向量m ∥向量n.则,2sinB*(-2cos^2(B/2)-(-√3)*(cos2B=0.
2sinB*[-(1+cosB)+√3cos2b=0.
-2sinB-2sinBcosB+√3cos2B=0.
-2sinB-sin2B+√3cos2B=0.
-[2(1/2)sin2B-(√3/2)cos2B=2sinB
-2[sin(2B-π/3)]=2sinB.
sin(π/3-2B=sinB.
∵∠B＜π/2.
∴π/3-2B=B,
3B=π/3.
∴ B=π/9.(=20°).
2.若b=2,求S△ABC.
S△ABC=(1/2)a*csinB.
由正弦定理,得：c/sinC=b/sinB.c=bsinC/sinB.
S△ABC=(1/2)a*(bsinC/sinB)*sinB.
=asinC.(b=2).
当sinC=1,∠C=π/2时,Smax=a (面积单位）.
式中,a=2*sin70°/sin20° .【B=20°,C=90°,A=70°】