(1) f(x)=cos3x/2 cosx/2 -sin3x/2 sinx/2-2sinxcosx=cos（3x/2 +x/2）-sin2x=cos2x-sin2x=-√2sin（2x-π/4）.f(x)的最少正周期是 2π/2,即π.(2) 当x∈[π/2,π]时,2x-π/4∈[3π/4,7π/4],在[3π/4,7π/4]内,使f(...