已知角α的终边经过点P(-x,-6),且cosα=-513,则1sinα+1tanα=______.-数学

题目简介

已知角α的终边经过点P(-x,-6),且cosα=-513,则1sinα+1tanα=______.-数学

题目详情

已知角α的终边经过点P(-x,-6),且cosα=-
5
13
,则
1
sinα
+
1
tanα
=______.
题型:填空题难度:中档来源:不详

答案

∵角α的终边经过点P(-x,-6),且cosα=-class="stub"5
13

∴cosα=class="stub"-x
x2+36
=-class="stub"5
13
,即x=class="stub"5
2
或x=-class="stub"5
2
(舍去),
∴P(-class="stub"5
2
,-6),
∴sinα=-
1-cos2α
=-class="stub"12
13

∴tanα=class="stub"sinα
cosα
=class="stub"12
5

class="stub"1
sinα
+class="stub"1
tanα
=-class="stub"13
12
+class="stub"5
12
=-class="stub"2
3

故答案为:-class="stub"2
3

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