化简sin(π-α)tan(5π2+α)cos(2π-α)cot(π2-α)=______.-数学

题目简介

化简sin(π-α)tan(5π2+α)cos(2π-α)cot(π2-α)=______.-数学

题目详情

化简
sin(π-α)tan(
2
+α)
cos(2π-α)cot(
π
2
-α)
=______.
题型:填空题难度:中档来源:不详

答案

原式=
sin(π-α)tan(2π+class="stub"π
2
+α)
cos(2π-α)cot(class="stub"π
2
-α)

=
sinαtan(class="stub"π
2
+α)
cos(-α)tanα

=class="stub"-sinαcotα
cosαtanα

=-cotα.
故答案为:-cotα

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