Question

此题求大神讲解,希望过程详尽些,(>^ω^

Answer 1

(1).

bsin(π/4+C)-csin(π/4+B)=a可化为：

bsin(A+C)-csin(A+B)=a 即

bsinB-csinC=a

sin^2(B)-sin^2(C)=sinA=√2/2

(1-cos2B)-(1-cos2C)=√2/2

cos2C-cos2B=√2/2

由和差化积公式

-2sin(C+B)sin(C-B)=√2/2

sin(C+B)=sinA=√2/2

sin(C-B)=-1

C-B= -π/2

B-C=π/2

(2)

a/sinA=2=2r==>r=1

B+C=135º

B-C=90º

B=112.5º

C=22.5º

b=sin112.5º=cos22.5º

c=sin22.5º

S=(1/2)bcsinA=(1/2)sin22.5cos22.5sin45=(1/4)sin45cos45=1/8