已知sin(2π+θ)tan(π+θ)tan(3π-θ)cos(π2-θ)tan(-π-θ)=1,则3sin2θ+3sinθcosθ+2cos2θ的值是()A.1B.2C.3D.6-数学

题目简介

已知sin(2π+θ)tan(π+θ)tan(3π-θ)cos(π2-θ)tan(-π-θ)=1,则3sin2θ+3sinθcosθ+2cos2θ的值是()A.1B.2C.3D.6-数学

题目详情

已知
sin(2π+θ)tan(π+θ)tan(3π-θ)
cos(
π
2
-θ)tan(-π-θ)
=1,则
3
sin2θ+3sinθcosθ+2cos2θ
的值是(  )
A.1B.2C.3D.6
题型:单选题难度:中档来源:不详

答案

sin(2π+θ)tan(π+θ)tan(3π-θ)
cos(class="stub"π
2
-θ)tan(-π-θ)

=
sinθtanθtan(π-θ)
-sinθtan(π+θ)
=class="stub"-sinθtanθtanθ
-sinθtanθ

=tanθ=1,
class="stub"3
sin2θ+3sinθcosθ+2cos2θ

=
3sin2θ+3cos2θ
sin2θ+3sinθcosθ+2cos2θ

=
3tan2θ+3
tan2θ+3tanθ+2
=class="stub"3+3
1+3+2
=1.
故选A.

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