(1-cotx+cscx)·(1-tanx+secx)如何解决?cscsec是什么来的?

Question

(1-cotx+cscx)·(1-tanx+secx)如何解决?
csc sec是什么来的?

Answer 1

tanx = sinx/cosx
cotx = cosx/sinx
cscx = 1/sinx
secx = 1/cosx
(1-cotx+cscx)(1-tanx+secx)
=(1-cosx/sinx+1/sinx)(1-sinx/cosx+1/cosx)
=((sinx-cosx+1)/sinx)((cosx-sinx+1)/cosx)
=(1-(sinx-cosx)^2)/(sinxcosx)
=(1-(sinx)^2+2sinxcosx-(cosx)^2)/(sinxcosx)
=2sinxcosx/(sinxcosx)
=2