Question

已知三角形ABC的三个内角A.B.C成等差数列,角B所对边b=根号3,且函数f（x）=2根号3sin²x+2sinxco

Answer 1

f（x）=2根号3sin²x+2sinxconx-根号3 在x=A取得最大值,得A = 75度

A,B,C成等差,所以, A=75

B = A+d

(1) -根号（3）-〉2

（2）

C = B+d= A+2d

3A + 3d = 180

A + d = 60, d = -15

B = 60

C = 45

a/sinA = b/sinB

a = b*sinA/sinB

S= 1/2 ab sinC = 1/2 b^2 sinAsinC/sinB