（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老师没有教过和差化积，能把和差化积那个部分的过程写给我吗和差化积公式sin α+sinβ=2sin[(α+β)/2]·cos[(α-β)/2]