tanπ/4=1=2tanπ/8/(1-tan²π/8)
令tanπ/8=a
2a/(1-a²)=1
a²+2a-1=0
a=tanπ/8>0
所以a=-1+√2
cosπ/4=√2/2=2cos²π/8-1
cos²π/8=(√2+2)/4
cosπ/8=√(√2+2)/2
所以原式=-1+√2+√(√2+2)/2