已知f(x)=sin^2+2√3sinxcosx-cos^2求f(x)单调增区间

Question

已知f(x)=sin^2+2√3sinxcosx-cos^2 求f(x)单调增区间

Answer 1

f(x)=sin²x+2√3sinxcosx-cos²x
=√3sin(2x)-cos(2x)
=2[(√3/2)sin(2x)-(1/2)cos(2x)]
=2sin(2x-π/6)
2kπ-π/2≤2x-π/6≤2kπ+π/2 (k∈Z)时,函数单调递增,此时kπ-π/6≤x≤kπ+π/3 (k∈Z)
函数的单调递增区间为[kπ-π/6,kπ+π/3] (k∈Z).