f(x)=4cos^2x+4sinxcosx-2
=2(2cos2x+1)+2sin2x-2
=4cos2x+2sin2x
=√(4²+2²)sin(2x+φ) (辅助角公式)
=2√5sin(2x+φ)
(1)最小正周期T=2π/2=π
(2)
∵-1≤sin(2x+φ)≤1
∴函数的最大值为2√5
f(x)=4cos^2x+4sinxcosx-2
=2(2cos2x+1)+2sin2x-2
=4cos2x+2sin2x
=√(4²+2²)sin(2x+φ) (辅助角公式)
=2√5sin(2x+φ)
(1)最小正周期T=2π/2=π
(2)
∵-1≤sin(2x+φ)≤1
∴函数的最大值为2√5