(1)展开f(x)=sin x*cos(7π/4)+cos x*sin(7π/4)+cos x*cos(7π/4)-sin x*sin(7π/4) =√2 *(sin x-cos x) =√2 *(sin x+sin (x+π/2)) 和差化积 =2√2 * sin(x+π/4) *cos(-π/4) =2sin(x+π/4) 最小正周期2π,最小值 -2 (2)cos(β-α)=cosβcosα+sinβsinα=4/5 cos(β+α)=cosβcosα-sinβsinα=-4/5 则cosβcosα=0 sinβsinα=4/5 又0<α>