好烦的三角函数
1. tan (π/4 –θ/2)=（1-tanθ/2）/(1+tanθ/2）=(cosθ/2-sinθ/2)/(cosθ/2+sinθ/2)=cosθ/(1+ sinθ)=
1.
cosθ=[cos(θ/2)]^2-[sin(θ/2)]^2=[cos(θ/2)+sin(θ/2)][cos(θ/2)-sin(θ/2)]
1+sinθ=sin(θ/2)^2+cos(θ/2)^2+2sin(θ/2)cos(θ/2)=[cos(θ/2)+sin(θ/2)]^2
所以cosθ/(1+sinθ)=[cos(θ/2)-sin(θ/2)]/[cos(θ/2)+sin(θ/2)]
分子分母同除以cos(θ/2),得：
cosθ/(1+sinθ)=[1-tan(θ/2)]/[1+tan(θ/2)]
而tan(π/4-θ/2)=[tan(π/4)-tan(θ/2)]/[1+tan(π/4)tan(θ/2)]
=[1-tan(θ/2)]/[1+tan(θ/2)]
所以cosθ/(1+ sinθ)= tan (π/4–θ/2)
2.
(1-sinθ)/(1+ sinθ)=[cos(θ/2)-sin(θ/2)]^2/[sin(θ/2)+cos(θ/2)]^2
=[1-tan(θ/2)]^2/[1+tan(θ/2)]^2
由前一小题知：tan(π/4-θ/2)=[1-tan(θ/2)]/[1+tan(θ/2)]
所以(1-sinθ)/(1+ sinθ)=[1-tan(θ/2)]^2/[1+tan(θ/2)]^2
=[tan(π/4-θ/2)]^2
