①f(x)=cosx(sinx √3cosx) (cosx-√3sinx)sinx =2sinxcosx √3cos^2 x-√3sin^2 x =sin2x √3cos2x =2sin(2x π/3) ②x∈[-π/2,π/2],则2x π/3∈[-2π/3,4π/3] 则2x π/3∈[-π/2,π/2]时,即x∈[-5π/12,π/12]时, f(x)递增.即f(x)递增区间为[-5π/12,π/12]
