tan(π/4+θ)+tan(π/4-θ)=4,cos2θ=?
问题描述：
tan(π/4+θ)+tan(π/4-θ)=4,cos2θ=?
答
设π/4+θ=A,则θ＝A－π/4,π/4-θ＝π/2-A,cos2θ=cos(2A-π/2)=sin(2A).
tan(π/4+θ)+tan(π/4-θ)=tanA+tan(π/2-A)=tanA+cotA.
然后切化弦,再通分得原式＝1／sinAcosA=2/sin2A=4
cos2θ=sin2A=1/2.