已知:x-2tana2+xtan2a2=0,y-1+tan2a2+ytan2a2=0.求证:cos2a=x2+y2-2sin2a.-数学

题目简介

已知:x-2tana2+xtan2a2=0,y-1+tan2a2+ytan2a2=0.求证:cos2a=x2+y2-2sin2a.-数学

题目详情

已知:x-2tan
a
2
+xtan2
a
2
=0,y-1+tan2
a
2
+ytan2
a
2
=0.求证:cos2a=x2+y2-2sin2a.
题型:解答题难度:中档来源:不详

答案

证明:∵x-2tanclass="stub"a
2
+xtan2class="stub"a
2
=0∴x=
2tanclass="stub"α
2
1+tan2class="stub"α
2
=sinα;
∵y-1+tan2class="stub"a
2
+ytan2class="stub"a
2
=0∴y=
1-tan2class="stub"α
2
1+tan2class="stub"α
2
=cosα.
则cos2α=1-2sin2α=sin2α+cos2α-2sin2α=x2+y2-2sin2a得证

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