Question

【题目】高中三角化简..头疼化简： 1+sinA+cosA ------------ 1+sinA-cosA 怎么化啊?

Answer 1

=(1+sinA+cosA)/(1+sinA-cosA)

=(1+cosA+sinA)/[(1-cosA)+sinA]

={2[cos(A/2)]^2+2sin(A/2)cos(A/2)}

/{2[sin(A/2)]^2+2sin(A/2)cos(A/2)|

=2(cos(A/2)[cos(A/2)+sin(A/2)]/{2sin(A/2)[sin(A/2)+cos(A/2)]|

=cos(A/2/sin(A/2)

=cot(A/2).