求证：2-2sin（a+3π\4）cos（a+π4）\cosa-sina=1+tana\1-tana

2-2sin（a+3π/4）cos（a+π/4）
=2-2sin(π/4-a)cos(a+π/4)
=2-2cos(π/2-(π/4-a))cos(a+π/4)
=2-2[cos(a+π/4)]^2
=2[sin(a+π/4)]^2
=1-cos(2a+π/2)
=1+cos(π/2-2a)
=1+sin2a
=(sina+cosa)^2
cosa-sina
[2-2sin(a+3π/4)cos(a+π/4)]/(cosa-sina)=(sina+cosa)^2/(cosa-sina)=cosa(1+tana)^2/(1-tana)