若tan(π4-θ)=3,则cos2θ1+sin2θ=______.-数学

题目简介

若tan(π4-θ)=3,则cos2θ1+sin2θ=______.-数学

题目详情

若tan(
π
4
-θ)
=3,则
cos2θ
1+sin2θ
=______.
题型:填空题难度:中档来源:不详

答案

∵tan(class="stub"π
4
-θ)=class="stub"1-tanθ
1+tanθ
=3,
∴tanθ=-class="stub"1
2

class="stub"cos2θ
1+sin2θ
=
cos2θ-sin2θ
sin2θ+cos2θ+2sinθcosθ
=
1-tan2θ
tan2θ+1+2tanθ
=
1-class="stub"1
4
class="stub"1
4
+1-1
=3.
故答案为:3

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