题目

求证(1-sinα)/cosα=tan(π/4-α/2)

提问时间：2021-02-22

答案

左边=(cosα/2-sinα/2)^2/[cos^2(α/2)-sin^2(α/2)]
=(cosα/2-sinα/2)/(cosα/2+sinα/2)
=(1-tanα/2)/(1+tanα/2)
=(tanπ/4-tanα/2)/(1+tanπ/4tanα/2)
=tan(π/4-α/2)