Question

Tanx+secx-1/tanx-secx+1=secx+tanx

Answer 1

tanx+secx-1/tanx-secx+1=secx+tanx is equivalent to 1+sinx/cosx.

Answer 2

We have to prove that,

`(\tan x+ \sec x-1)/(\tan x- \sec x + 1)=\secx+\tan x`

L.H.S.

`(\tan x+ \sec x-1)/(\tan x- \sec x + 1)`

`=(\tan x+ \sec x-(\sec^2 x-\tan^2x))/(\tan x- \sec x + 1)`

( ∵ sec² x - tan² x = 1 )

`=(\tan x+ \sec x-(\sec x-\tan x)(\sec x+\tan x))/(\tan x- \sec x + 1)`

( ∵ a² - b² = ( a + b ) ( a - b ) )

`=((\tan x+\sec x)(1-\sec x+\tan x))/(\tan x-\sec x + 1)`

`=\tan x+\sec x`

= R.H.S

Hence, proved.....