已知cos^2 (a/2)=sin a (a ≠ π +2kπ ,k ∈ Z ),则tan (a/2)=?急,会的帮个忙,

题目

已知cos^2 (a/2)=sin a (a ≠ π +2kπ ,k ∈ Z ),则tan (a/2)=?急,会的帮个忙,

答案

解:
cos^2 (a/2)=sin a
--> cos^2 (a/2)=2sin(a/2) * cos(a/2) (1)
因为:a ≠ π +2kπ
所以:a/2 ≠ π/2 +kπ
--> cos(a/2) ≠ 0
--> (1)等式两边同除以cos^2(a/2) --> tan(a/2)=1/2
希望能帮助你哈