∫Mn = sin(A-B)+sin(π/2-A)* 2 sinb
=sin(A-B)+cosA*2sinB
=sinAcosB-sinBcosA+2sinBcosA
=sinAcosB+sinBcosA
=sin(A+B)
=sinC
∫Mn =-sin2C
∴sinC=-sin2C=-2sinCcosC
CosC=- 1/2。
∴C=2π/3
2、∫S△ABC = 1/2 * absinC =√3/4 * ab =√3
∴ab=4
∫sinA+sinB = 3/2 sinc
According to sine theorem: a/sinA=b/sinB=c/sinC has:
a+b=3c/2
Also: according to the cosine theorem:
cosC=(a? +b? -c? )/2ab
=[(a+b)? -2ab-c? ]/2ab
=(9c? /4-8-c? )/8
=5c? /32- 1
=- 1/2
Is that 5c? /32= 1/2
c? = 16/5
Solution: c=4√5/5
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