1、
正弦定理
a/sinA=c/sinC
sinC=c×sinA/a
=(√2×√14/4)/2
=√7/4
由余弦定理
a²=b²+c²-2bc×cosA
4=b²+2-2×√2×(-√2/4)b
4=b²+2+b
b²+b-2=0
(b+2)(b-1)=0
b=1
b=-2(舍去）
2、
cos(2A+π/3)
=cos2Acoc60°-sin2Asin60°
=1/2cos2A-√3/2sin2A
=1/2(2cos²A-1)-√3/2×2sinAcosA
=1/2×2×(-√2/4)²-1/2-√3/2×2×√14/4×(-√2/4)
=2/16-1/2+√3×√14×√2/16
=1/8-1/2+√21/8
=(√21-3)/8