求证tan(a/2)-1/(tana/2)=-2/tana

题目详情

▼优质解答

答案和解析

tan(a/2)-1/(tana/2)
=sin(a/2)/cos(a/2)-cos(a/2)/sin(a/2)
通分
=[sin²(a)-cos²(a/2)]/[sin(a/2)cos(a/2)]
=-cosa/[(sina)/2]
=-2cosa/sina
=-2/tana
证毕

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