已知5sin2a=sin2°,则tan(a+1°)tan(a-1°)=______.-数学

题目简介

已知5sin2a=sin2°,则tan(a+1°)tan(a-1°)=______.-数学

题目详情

已知5sin2a=sin2°,则
tan(a+1°)
tan(a-1°)
=______.
题型:填空题难度:中档来源:不详

答案

5sin2a=sin2°
5sin[(a+1°)+(a-1°)]
=sin[(a+1°)-(a-1°)]
=5sin(a+1°)cos(a-1°)+5cos(a+1°)sin(a-1°)
=sin(a+1°)cos(a-1°)-cos(a+1°)sin(a-1°)
∴4sin(a+1°)cos(a-1°)=-6cos(a+1°)sin(a-1°)
两边除以cos(a-1°)cos(a+1°):
得4tan(a+1°)=-6tan(a-1°)
tan(a+1°)
tan(a-1°)
=-class="stub"6
4
=-class="stub"3
2

故答案为-class="stub"3
2

更多内容推荐