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<π/2,∴ α=5π/12,即A=5π/12,又B=π/12,故C=π/2
(解答到这里, 与题中锐角三角形不符; 题中还有f(α)、F(A)前后函数不相同)若按C=π/2的情况, a/c=sinA=(√2 +√6)/4.... |
