Question

若0<α<π/2,则根号(1-2sinα/2cosα/2)+根号(1+2sinα/2cosα/2)=_______

Answer 1

√2/2sinα-√2/2cosα
=sinαcos45°-cosαsin45°
=sin(α-45)
或=sin45sinα-cos45cosα
=-(cos45cosα-sin45sinα)
=-cos(45-α)
下面同理
运用的是正弦于余弦两角和与差
1/2sinα+√3/2cosα
=sinαcos30°+cosαsin30°
=sin(α+30)
√3sinα-cosα
=2(√3/2sinα-1/2cosα)
=2(sinαcos30°-cosαsin30°)
=2sin(α-30)