已知tanx=3,求下列各式的值:(1)y1=2sin2x-5sinxcosx-cos2x;(2)y2=3cosx-sinx3cosx+sinx.-数学

题目简介

已知tanx=3,求下列各式的值:(1)y1=2sin2x-5sinxcosx-cos2x;(2)y2=3cosx-sinx3cosx+sinx.-数学

题目详情

已知tanx=3,求下列各式的值:
(1)y1=2sin2x-5sinxcosx-cos2x;
(2)y2=
3
cosx-sinx
3
cosx+sinx
题型:解答题难度:中档来源:不详

答案

(1)y1=2sin2x-5sinxcosx-cos2x=
2sin2x-5sinxcosx-cos2x
sin2x+cos2x
=
2tan2x-5tanx-1
tan2x+1
=class="stub"18-15-1
10
=class="stub"1
5

(2)y2=
3
cosx-sinx
3
cosx+sinx
=
3
-tanx
3
+tanx
=
3
-3
3
+3
=
3
-2

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