Question

sec2 x - tan2xHere is the proof of= sec X -tan x.sec x + tan xWhat is the missing line?1.O(sec x - tan x)(sec x - tan x)sec x + tan xO(sec x + tan x)(sec x + tan x)sec x + tan x(sec x - tan x)(sec x + tan x)sec x + tan xO(sec x - tan x)(sec x + tan x)sec X -tan x

Answer 1

Given:

`(\sec ^2x-\tan ^2x)/(\sec x+\tan x)`

Sol:

`(\sec ^2x-\tan ^2x)/(\sec x+\tan x)`

Use the formula:

`(a+b)(a-b)=a^2-b^2`

Then:

`\begin{gathered} =(\sec ^2x-\tan ^2x)/(\sec x+\tan x) \\ =((\sec x-\tan x)(\sec x+\tan x))/(\sec x+\tan x) \\ =\sec x-\tan x \end{gathered}`

So missing line is:

`=((\sec x-\tan x)(\sec x+\tan x))/(\sec x+\tan x)`