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Mathematical trigonometric function exercise
1, inch △ABC

∫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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