用半角公式呀!也可倍角公式推得.
cos45=2(cos22.5)^2-1=1-2(sin22.5)^2
解得sin22.5=[√（2-√2）]/2,
cos22.5=[√（2+√2）]/2,
tan22.5=sin22.5/cos22.5
=2sin22.5cos22.5/2*(cos22.5)^2
=sin45/(1+cos45)
=(1-cos45)/sin45
=√2-1