1、
S=c^2-(a-b)^2
c^2=a^2+b^2-2abcosC
S=-2abcosC+2ab=2ab(1-cosC)=4absin^2C/2=0.5absinC=absinC/2cosC/2
tanC/2=1/4,2sinC/2cosC/2=sinC=(2*tanC/2)/(1+tan^2C/2)
=(1/2)/(1+1/16)=8/17
S=0.5absinC=4ab/17
a+b=2>=2√(ab),ab<=1,a=b=1等腰三角形，顶角C
S<=4/17
Smax=4/17
2、很乱
（1）
4sinBsin^2(45°+B/2)+cos2B=2sinB[1-cos(90°+B)]+cos2B
=2sinB+2sin^2B+cos2B=2sinB+1=1+√3
sinB=√3/2
B=60°,或B=120°
（2）
S=0.5acsinB=2c*√3/2=c√3=5√3,c=5
b^2=a^2+c^2-2accosB=25+16±20
b1=√21,b2=√61