已知tan(a+π\4)=1\2,求(1)sin2a的值(2)sin2a-cos'2a\1+cos2a的值

tan(a+π/4) = (tana+1)/(1 - tana) = 1/2
解得 tana = - 1/3
sin2a = 2sinacosa
= 2sinacosa / ( sin²a +cos²a)
= 2tana / (tan²a +1) （分子分母同除以 cos²a）
= 2*(-1/3) / [ (-1/3)²+1]
= - 3/5
(sin2a+cos2a) / (1+cos2a)
= (2sinacosa+cos²a - sin²a) / (2cos²a)
= tana + 1/2 - tan²a
= - 1/3 + 1/2 - (-1/3)²
= 1/18