Search: Verify the identity: tanx/secx-1=secx+1/tanx

Verify the identity: tanx/secx-1=secx+1/tanx verify: tanx secx = -2tanx verify sinx/secx = 1/tanx+cotx 1/tanx-secx+ 1/tanx+secx=-2tanx so this is what I did: =tanx+secx+tanx-secx =(sinx/cosx)+ (1/... secx+tanx/secx- tanx = 1+2sinx+sin^2x/ cos^2x (cosxcotx/secx+tanx)+(sinx/secx-tanx) proof that tanx + secx -1/tanx - secx+1 = 1+sinx/cosx secx/secx-tanx=sec^2x+ secx+tanx (1/tanx-secx))+(1/(tanx+secx))=-2tanx how does secx(tanx + tan^2x- sec^2x) simplified to sec x (tanx -1)?