解cos2(π-α)+sin(π+α)cos(π-α)+2sin2(α-π)
=cos（2π-2α)+[-sin(α)][-cos(α)]+2sin(2α-2π)
=cos2α+sin(α)cos(α)-2sin(2π-2α)
=cos2α+sin(α)cos(α)-2sin(-2α)
=cos2α+1/2*2*sin(α)cos(α)+2sin(2α)
=cos2α+1/2sin(2α)+2sin(2α)
=cos2α+5/2sin(2α)
=（1-tan²a）/(1+tan²a)+5/2*2tana/(1+tan²a)
=（1-(√2/2)²）/(1+(√2/2)²)+5/2*2(√2/2)/(1+(√2/2)²)
=(1-1/2)/(1+1/2)+5√2/2/(1+1/2)
=1/3+5√2/3
=(1+5√2)/3