已知tanα=2,α∈(π,3π2),求:(1)sin(π+α)+2sin(3π2+α)cos(3π-α)+1;(2)sinαcosα.-数学

题目简介

已知tanα=2,α∈(π,3π2),求:(1)sin(π+α)+2sin(3π2+α)cos(3π-α)+1;(2)sinαcosα.-数学

题目详情

已知 tanα=2,  α∈(π,
2
)
,求:(1)
sin(π+α)+2sin(
2
+α)
cos(3π-α)+1
;(2)sinαcosα.
题型:解答题难度:中档来源:不详

答案

∵tanα=2,α∈(π,class="stub"3π
2

∴sinα=-class="stub"2
5
,cosα=-class="stub"1
5

(1)原式=class="stub"-sinα-2cosa
-cosα+1
=
class="stub"2
5
+ class="stub"2
5
class="stub"1
5
+1
=class="stub"4
1+
5
=
5
-1

(2)sinαcosα=class="stub"sinαcosα
sin2α +cos2α

=class="stub"tanα
1+tan2α
=class="stub"2
5

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