在三角形ABC,设A,B,C的对边分别是a,b,c,∠C=60°,c=√3.（1）(a+2√3cosA)sinB的值.（

c/sinC=a/sinA=b/sinB,a/sinA=√3/sin60
a=2sinA,b=2sinB
(a+2√3cosA)/sinB=(2sinA+2√3cosA)/sinB
=2(sinA+√3cosA)/sin(120-A)
=2(sinA+√3cosA)/(sin120cosA-cos120sinA)
=2(sinA+√3cosA)/(√3/2cosA+1/2sinA)
=4
S=1/2cbsinA=1/2*√3*√3/3*2sinB=sinB
sinB=sin(A+C)=sinAcosc+cosAsinc
sinA=√3/3,cosA=2√2/3,sinc=sin60=√3/2,cosc=cos60=1/2
sinB=sin(A+C)=sinAcosc+cosAsinc=√3/3*1/2+2√2/3*√3/2
=(√3+2√6)/6
S=1/2cbsinA=1/2*√3*√3/3*2sinB=sinB=(√3+2√6)/6

∵a=c.sinAsinC ∴a=2sinA ∵C=60º∴A+B=120º
∴原式=(2sinA+2√3cosA)sin(120º-A)
=2√3sinAcosA+sin²A+3cos²A
=√3sin2A+2cos²A+cos²A+sin²A
=√3sin2A+2cos...

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