因为cos(α+π/4)=3/5,所以sin(α+π/4)=4/5.
所以sinα=sin[(α+π/4)-π/4]
=sin(α+π/4)cos(π/4)-cos(α+π/4)sin(π/4)
=√2/2*(4/5-3/5)
=√2/10.