已知π2<α<π,且sin(π-α)=45(1)求sin(2π+α)tan(π-α)cos(-π-α)sin(3π2-α)cos(π2+α)的值.(2)求sin(π-α)+cos(-α)tan(π+α

题目简介

已知π2<α<π,且sin(π-α)=45(1)求sin(2π+α)tan(π-α)cos(-π-α)sin(3π2-α)cos(π2+α)的值.(2)求sin(π-α)+cos(-α)tan(π+α

题目详情

已知
π
2
<α<π,且sin(π-α)=
4
5

(1)求
sin(2π+α)tan(π-α)cos(-π-α)
sin(
2
-α)cos(
π
2
+α)
的值.
(2)求
sin(π-α)+cos(-α)
tan(π+α)
的值.
题型:解答题难度:中档来源:不详

答案

class="stub"π
2
<α<π,sin(π-α)=sinα=class="stub"4
5

∴cosα=-
1-sin2α
=-class="stub"3
5
,故tanα=class="stub"sinα
cosα
=-class="stub"4
3

(Ⅰ)由诱导公式可得
sin(2π+α)tan(π-α)cos(-π-α)
sin(class="stub"3π
2
-α)cos(class="stub"π
2
+α)

=
sinα•(-tanα)•(-cosα)
-cosα•(-sinα)
=-tanα=class="stub"4
3

(Ⅱ)由诱导公式可得
sin(π-α)+cos(-α)
tan(π+α)

=class="stub"sinα+cosα
tanα
=
class="stub"4
5
-class="stub"3
5
-class="stub"4
3
=-class="stub"3
20

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