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

题目

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

答案

因为
（sina-cosa+1）/（sina+cosa-1）-tan(a/2+π/4)
=（sina-cosa+1）/（sina+cosa-1）-[1-cos(a+π/2)]/sin(a+π/2)]
=（sina-cosa+1）/（sina+cosa-1）-(1+sina) / cosa
=[cosa（sina-cosa+1）-(1+sina)（sina+cosa-1）] / [ cosa（sina+cosa-1）]
=[cosasina-cos²a+cosa-(sina+cosa-1+sin²a+cosasina-sina）] / [ cosa（sina+cosa-1）]
=[-cos²a+1-sin²a] / [ cosa（sina+cosa-1）]
=0
左边-右边=0
所以,
（sina-cosa+1）/（sina+cosa-1）=tan(a/2+π/4)成立