已知函数f(x)=2cos(x-2π/3)+2cosx,x∈[π/2,π] 求函数f(x)的值域.求详解,
问题描述：
已知函数f(x)=2cos(x-2π/3)+2cosx,x∈[π/2,π] 求函数f(x)的值域.求详解,
答
f(x)=2cosxcos(2π/3)+2sinxsin(2π/3)+2cosx
=√3sinx+cosx
=2sin(x+π/6)
∵ x∈[π/2,π]
则 x+π/6∈[2π/3,7π/6]
∴ sin(x+π/6)∈[-1/2,√3/2]
即2sin(x+π/6)∈[-1,√3]f(x)=2cosxcos(2π/3)+2sinxsin(2π/3)+2cosx=√3sinx+cosx 这一步怎么变化过来的没懂。展开化简就行