1+2sin(π−2)•cos(π−2)

=

[sin(π−2)+cos(π−2)]2

=|sin（π-2）+cos（π-2）|=|sin2-cos2|
∵sin2>0，cos2<0，
∴sin2-cos2>0，
∴

1+2sin(π−2)•cos(π−2)

=sin2-cos2
故选C