Question

高中数学三角变换

化简（1+sina-cosa)/(1+sina+cosa)=

请告诉我答案及详细转换过程，谢谢！

Answer 1

cosa=1-2sin^2(a/2)
cosa=2cos^2(a/2)-1分别代入上式中则有2sin(a/2)(sin(a/2)+cos(a/2))/2(cos(a/2)(sin(a/2)+cos(a/2))=sin(a/2)/cos(a/2)=tan(a/2)

Answer 2

1-cosa=2sin(a/2)^2
1+cosa=2cos(a/2)^2
sina=2sin(a/2)cos(a/2)
（1+sina-cosa)/(1+sina+cosa)
=[2sin(a/2)^2+2sin(a/2)cos(a/2)]/[2cos(a/2)^2+2sin(a/2)cos(a/2)]
=sin(a/2)/cos(a/2)
=tan(a/2)

Answer 3

=（sina+1)²-cosa²=1+2sina+sina²-cosa²=1+2sina+2sina²-1=2(1/2+sina)²-1/2