Question

化简

sin(π-α)tan( 5π 2 +α)

cos(2π-α)cot( π 2 -α)

=______．

Answer 1

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