∵α为锐角
∴cosα>0
∵tanα=√2-1
==>sinα/cosα=√2-1
==>sinα=(√2-1)cosα
==>((√2-1)cosα)^2+(cosα)^2=1 (∵(sinα)^2+(cosα)^2=1)
==>(cosα)^2=(2+√2)/4
∴cosα=√(2+√2)/2.