首页 > 已知：sin(θ+3π)=-23，则tan(-5π-θ)•cos(θ-2π)•sin(-3π-θ)tan(7π2+θ)•sin(-4π+θ)•cot(-θ-π2)+2tan(6π-θ)•cos(-π+

已知：sin(θ+3π)=-23，则tan(-5π-θ)•cos(θ-2π)•sin(-3π-θ)tan(7π2+θ)•sin(-4π+θ)•cot(-θ-π2)+2tan(6π-θ)•cos(-π+

题目简介

已知：sin(θ+3π)=-23，则tan(-5π-θ)•cos(θ-2π)•sin(-3π-θ)tan(7π2+θ)•sin(-4π+θ)•cot(-θ-π2)+2tan(6π-θ)•cos(-π+

题目详情

已知：sin(θ+3π)=-
2
3
，则
tan(-5π-θ)•cos(θ-2π)•sin(-3π-θ)
tan(
7π
2
+θ)•sin(-4π+θ)•cot(-θ-
π
2
)
+2tan(6π-θ)•cos(-π+θ)=______．
题型：填空题难度：中档来源：不详

答案

因为sin(θ+3π)=-class="stub"2
3
，
∴sinθ=class="stub"2
3
．
∵
tan(-5π-θ)•cos(θ-2π)•sin(-3π-θ)
tan(class="stub"7π
2
+θ)•sin(-4π+θ)•cot(-θ-class="stub"π
2
)
+2tan(6π-θ)•cos(-π+θ)
=
tan(-θ)•cosθ•sinθ
-cotθ•sinθ•(-tanθ)
+2（-tanθ）•（-cosθ）
=-sinθ+2sinθ
=sinθ=class="stub"2
3
．
故答案为：class="stub"2
3
．

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