f(x)=sin2x+2根号3cos平方x+3-根号3求最小正周期(2)在三角形ABC中若f(A)=f(B)=3+根号3且三角形面积为根...

题目

f(x)=sin2x+2根号3cos平方x+3-根号3求最小正周期(2)在三角形ABC中若f(A)=f(B)=3+根号3且三角形面积为根...
f(x)=sin2x+2根号3cos平方x+3-根号3求最小正周期(2)在三角形ABC中若f(A)=f(B)=3+根号3且三角形面积为根号3求c的值

答案

(1)
f(x) =sin2x+2√3(cosx)^2+3-√3
= sin2x+√3cos2x +3
= 2sin(2x+π/3) +3
最小正周期=π
(2)
f(A)=f(B)=3+√3
A1=√3
To find:c
f(A) = 2sin(2A+π/3) +3 = 3+√3
sin(2A+π/3)=√3/2
2A+π/3 = 2π/3
A=π/6
B=π/6
C=2π/3
by sine rule
a/sinA = c/sinC
a = (c/sinC)sinA = c/√3
b=c/√3
A1= (1/2)absinC
√3 = (1/2) (c^2/3)(√3/2)
c^2=12
c= 2√3