p=cosacosb
q=cos²[(a+b)/2]=[1+cos(a+b)]/2=[cosacosb-sinasinb+1]/2
∴p-q=[cosacoab+sinasinb-1]/2
=[cos(a-b)-1]/2
∵cos(a-b)≤1
∴p-q≤0
即p≤q
p=cosacosb
q=cos²[(a+b)/2]=[1+cos(a+b)]/2=[cosacosb-sinasinb+1]/2
∴p-q=[cosacoab+sinasinb-1]/2
=[cos(a-b)-1]/2
∵cos(a-b)≤1
∴p-q≤0
即p≤q