(1)已知sin(π4-α)=513,α∈(0,π4),求cos2αcos(π4+α)的值.(2)已知tanα=-12,求2sin(2α-π4)+11+tanα的值.-数学

题目简介

(1)已知sin(π4-α)=513,α∈(0,π4),求cos2αcos(π4+α)的值.(2)已知tanα=-12,求2sin(2α-π4)+11+tanα的值.-数学

题目详情

(1)已知sin(
π
4
-α)=
5
13
,α∈(0,
π
4
),求
cos2α
cos(
π
4
+α)
的值.
(2)已知tanα=-
1
2
,求
2
sin(2α-
π
4
)+1
1+tanα
的值.
题型:解答题难度:中档来源:不详

答案

(1)∵sin(class="stub"π
4
-α)=class="stub"5
13
,α∈(0,class="stub"π
4

∴cos(class="stub"π
4
-α)=class="stub"12
13

sin(class="stub"π
4
+α)=class="stub"12
13

class="stub"cos2α
cos(class="stub"π
4
+α)
=
sin(class="stub"π
2
+2α)
cos(class="stub"π
4
+α)
=2sin(class="stub"π
4
+α)=class="stub"24
13

(2)∵tanα=-class="stub"1
2

2
sin(2α-class="stub"π
4
)+1
1+tanα
=class="stub"sin2α-cos2α+1
1+tanα
=
2sinαcosα+2sin2α
1+class="stub"sinα
cosα
=2sinαcosα=class="stub"2sinαcosα
sin2α+cos2α
=class="stub"2tanα
1+tan2α
=-class="stub"4
5

更多内容推荐