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

题型：填空题难度：一般来源：不详

化简

sin(π-α)tan( 5π 2 +α)

cos(2π-α)cot( π 2 -α)

=______．

答案

原式=

sin(π-α)tan(2π+ π 2 +α)

cos(2π-α)cot( π 2 -α)

=

sinαtan( π 2 +α)

cos(-α)tanα

=

-sinαcotα

cosαtanα

=-cotα．
故答案为：-cotα