Question

求证(1-sina+cosa)/(1+sina+cosa)=tan(π/4-a/2)

Answer 1

(1-sina+cosa)/(1+sina+cosa)=[2(cosa/2)^2-2sina/2*cosa/2)/[2sina/2cosa/2+2(cosa/2)^2]

=[cosa/2-sina/2]/[cosa/2+sina/2]=[1-tana/2]/[1+tana/2]

=[tan(p/4)-tana/2]/[1+tan(p/4)tana/2]

=tan(p/4-a/2)

其中：p表示派