Question

设函数f(x)=2cosxsin(x+π／6)+2sinxcos(x+π／6)⑴当x属于0到2分之π的闭区间求f（x）的

Answer 1

f(x)=2cosxsin(x+π／6)+2sinxcos(x+π／6）

=2sin(2x+π/6),

(1)x∈[0,π/6],

∴2x+π/6∈[π/6,π/2],

∴f(x)的值域是[1,2].

(2)f(A)=2sin(2A+π/6)=1,

∴sin(2A+π/6)=1/2,

2A+π/6=5π/6,

A=π/3,

由余弦定理,7=b^+c^-bc,

(1/2)bc*√3/2=（3/2）√3,bc=6,

∴(b+c)^=25,

b+c=5.