Question

在△ABC中,A,B,C的对边为a,b,c.且a,b,c成等比数列,求：①∠B的范围②求f(B)=sinB+根号3cos

Answer 1

a/sinA=b/sinB=c/sinC

b^2=ac

(sinB)^2=sinA*sinC=-（cos(A+C)-cos(A-C)）/2=(cosB+cos(A-C))/2

令cosB=x

1-x^2=(x+cos(A-C))/2

2x^2+x+cos(A-C)-1=0

2(x+1/4)^2+cos(A-C)-9/8=0

2(x+1/4)^2=9/8-cos(A-C)

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