化简(cscα-sinα)(secα-cosα)(tanα+cotα)

化简(cscα-sinα)(secα-cosα)(tanα+cotα)
化简(cscα-sinα)(secα-cosα)(tanα+cotα)

化简(cscα-sinα)(secα-cosα)(tanα+cotα)
(cscα-sinα)(secα-cosα)(tanα+cotα)
=(cosα-sinα)(sin^2α/cosα)((1+tan^2α)/tanα)
=(cosα-sinα)(sin^2α/cosα)(1/cosαtan^2α)
=(cosα-sinα)(sin^2α/cos^2αtanα)
=(cosα-sinα)(sin^3α/cos^4α)
=tan^3α-tan^4α

(cscα-sinα)(secα-cosα)(tanα+cotα)
=(1/sinα-sinα)(1/cosα-cosα)(sinα/cosα+cosα/sinα)
=[(1-sin²α)/sinα]×[(1-cos²α)/cosα]×[(sin²α+cos²α)/sinαcosα]
=(cos²α/sinα)×(sin²α/cosα)×(1/sinαcosα)
=1