tan(a+π/4)=k,则cos2a=
问题描述：
tan(a+π/4)=k,则cos2a=
答
由 tan 的和角公式：
tan(a+π/4)
=(tana+tanπ/4)/(1-tanatanπ/4)
=(1+tana)/(1-tana)
=k
所以 tana = (k-1)/(k+1).sina/cosa = tana = (k-1)/(k+1).
结合 (sina)^2+(cosa)^2=1 即知 (sina)^2 = (k-1)^2/(2k^2+2).
再由倍角公式即知 cos2a = 1-2(sina)^2 = 2k/(k^2+1).