secx/sinx-cosx/sinx
*secx=1/cosx*
(1/cosx)/sinx-cosx/sinx
(1/cosx-cosx)/sinx
(1/cosx-cos^2x/cosx)/sinx
(1-cos^2x/cosx)/sinx
*cos^2x+sin^2x=1 -------->sin^2x=1-cos^2x*
(sin^2x/cosx)/sinx -------------> (sin^2x/cosx)•(1/sinx)
= (sin^2x)/sinxcosx
*sinx/cosx=tanx*
=tanx