tanα(cosα-sinα)+(sinα+tanα)/(cotα+cscα)
=(sinα/cosα)(cosα-sinα)+(sinα+sinα/cosα)/(cosα/sinα+1/sinα)
=sinα-(sinα)^2/cosα+[(sinαcosα+sinα)sinα]/[(cosα+1)cosα]
=sinα-(sinα)^2/cosα+[(sinα)^2cosα+(sinα)^2]/[cosα+1)cosα]
=sinα-{[(sinα)^2*(coα+1)]-[(sinα)^2cosα+(sinα)^2]}/[cosα+1)cosα]
=sinα-0
=sinα