(sinx+cosx)(tan^2x+1/tanx)-[1/cosx+1/sinx]
=(sinx+cosx ) (tan^2x+1/tanx)-[(sinx+cosx)/sinxcosx]
=(sinx+cosx)[tanx+(1/tanx)-(1/sinxcosx)]
=(sinx+cosx)[(sinx/cosx)+(cosx/sinx)-(1/sinxcosx)]
=(sinx+cosx)[(1/sinxcosx)-(1/sinxcosx)]
=0