Question

Establish the identity
(sec x+tan x)(sec x-tanx)=1

Answer 1

first, we can use the difference squares formula :
(a+b)(a-b) = a^2 - b^2

Answer 2

so,
(sec x+tan x)(sec x-tanx) = sec^2 (x) - tan^2 (x), right ?

Answer 3

then use the identity :
sec^2 (x) = tan^2 (x) + 1

Answer 4

therefore,
(sec x+tan x)(sec x-tanx)
= sec^2 (x) - tan^2 (x)
= tan^2 (x) + 1 - tan^2 (x)
= 1

Answer 5

thank you =)

Answer 6

you're welcome :)