`(secxsecy+tanxtany)^2-(secxtany+tanxsecy)^2=1` Prove it

The simplified value of (secxsecy+tanxtany)^(2)-(secxtany+tanxsecy)^(2) is :

(secx.secy + tanx.tany)^(2)-(secx.tany + tanx.secy)^(2) in its simplest form, is

(tan x+tan y)/(1-tanxtany) =……………

Prove that tan(x+y)=(tanx+tany)/(1-tanxtany)

If xy b) tan^-1(frac(x+y)(1-xy)) c) (tanx+tany)/(1-tanxtany) d) (tanx-tany)/(1-tanxtany)

Prove that (1tanx)^2+(1-cotx)^2=(secx-cosecx)^2

Prove that: tanA(1+sec2A)=tan2A

Prove that: tanA(1+sec2A)=tan2A

Prove that, (1+tanA)^2 + (1-tanA)^2 = 2sec^2A

i) Prove that: (1+tan^(2)A)/(1-tan^(2)A) xx (2 cos^(2) A-1)=1 ii) Prove that: (tantheta)/(1+cottheta)+(cottheta)/(1+tantheta) = "cosec"theta.sectheta-1