若cos(π4+α)=35,且17π12<α<7π4(1)求sin2α的值;(2)求1+tanα1-tanα的值.-数学

题目简介

若cos(π4+α)=35,且17π12<α<7π4(1)求sin2α的值;(2)求1+tanα1-tanα的值.-数学

题目详情

cos(
π
4
+α)=
3
5
,且
17π
12
<α<
4

(1)求sin2α的值;
(2)求
1+tanα
1-tanα
的值.
题型:解答题难度:中档来源:不详

答案

(1)∵class="stub"17π
12
<α<class="stub"7π
4

class="stub"10π
3
<2α+class="stub"π
2
<4π
,又cos(class="stub"π
4
+α)=class="stub"3
5

sin2α=-cos(2α+class="stub"π
2
)=1-2cos2(α+class="stub"π
4
)=class="stub"7
25

(2)∵class="stub"17π
12
<α<class="stub"7π
4

class="stub"π
4
+α∈(class="stub"4π
3
,2π)
,又cos(class="stub"π
4
+α)>0

class="stub"π
4
+α∈(class="stub"3π
2
,2π)

∴sin(class="stub"π
4
+α)=-class="stub"4
5
,tan(class="stub"π
4
+α)=-class="stub"4
3

tan(class="stub"π
4
+α)
=class="stub"1+tanα
1-tanα
=-class="stub"4
3

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