若sinθ+cosθsinθ-cosθ=2,则sin(θ-5π)•sin(3π2-θ)=______.-数学

题目简介

若sinθ+cosθsinθ-cosθ=2,则sin(θ-5π)•sin(3π2-θ)=______.-数学

题目详情

sinθ+cosθ
sinθ-cosθ
=2,则sin(θ-5π)•sin(
2
-θ)
=______.
题型:填空题难度:中档来源:不详

答案

class="stub"sinθ+cosθ
sinθ-cosθ
=2,得到sinθ+cosθ=2sinθ-2cosθ化简得tanθ=3;
则sin(θ-5π)•sin(class="stub"3π
2
-θ)
=(-sinθ)(-cosθ)=sinθcosθ=class="stub"1
2
sin2θ=class="stub"1
2
×class="stub"2tanθ
1+tan2θ
=class="stub"3
1+32
=class="stub"3
10

故答案为:class="stub"3
10

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