已知a为第二象限角,化简.

Question

已知a为第二象限角,化简.

Answer 1

第二象限的正弦为正,余弦为负
cosα√[(1-sinα)/(1+sinα)}+sinα√[(1-cosα)/(1+cosα)]
=cosα√[(1-sinα)^2/(1-sinα^2)}+sinα√[(1-cosα)^2/(1-cosα^2)]
=-√(1-sinα)^2+√(1-cosα)^2
=-|1-sinα|+|1-cosα|
=-1+sinα+1-cosα ( 1-sinα≥0,1-cosα≥0)
=sinα-osα
(=√2sin(α-π/4)