Question

设函数f（x）=6cos^2x-2√3sinxcosx,若锐角α满足f（α）=3-2√3,在锐角三角形

Answer 1

由题意,f(x)=6cos^2x-2√3sinxcosx,

化简得,f(x)=3cos2x -√3sin2x +3,

即有f(α)=3cos2α -√3sin2α +3=3-2√3,

化简得,1/2·sin2α -√3/2·cos2α=1,

可得,sin(2α-π/3)=1,

有2α-π/3=2kπ+π/2,k∈N,

∵ α