sin(π/8)=sin[(1/2)×(π/4)]=√[(1-cosπ/4)/2]=√[(1-√2/2)/2]=[√(2-√2)]/2;cos(π/8)=cos[(1/2)×(π/4)]=√[(1+cosπ/4)/2]=√[(1+√2/2)/2]=[√(2+√2)]/2;tan(π/8)=sin(π/8)/cos(π/8)=[√(2-√2)]/[√(2+√2)]=√[(2-√2)/(2+√2)]=√(3-2√2)=√(√2-1)²=(√2)-1.【你好像把分数的分子分母写颠倒了。】