Question

(1+sina)/cosa=(1+tana/2)/(1-tana/2)

Answer 1

证明：
左边=[1+2tana/2/(1+tan^2a/2)]/[(1-tan^2a/2)/(1+tan^2a/2)]
=[(1+tan^2a/2+2tana/2)/(1+tan^2a/2)]/[(1-tan^2a/2)/(1+tan^2a/2)]
=(1+tana/2)^2/[(1+tana/2)(1-tana/2)]
=(1+tana/2)/(1-tana/2)
=右边
原式得证!

Answer 2

它省略好多(1+sina)/cosa利用正弦平方+余弦平方=1分子是正弦二倍角分母是余弦二倍角公式=(sin^2a/2+cos^2a/2+2sina/2*cosa/2)/(cos^2a/2-sin^2a/2)分子分母同除cos^2a/2=(1+tan^2a/2+tana/2)/(1-tan^2a/2)分子是完全平方式分母是平方差=(1+tan^2a/2)^2/(1-tan^2a/2)=(1+tana/2)/(1-tana/2)手机提问的朋友在客户端右上角评价点【满意】即可