Question

Prove the identity

secx-1/ tan x= tanx/ secx+1
To verify the​ identity, start with the left side and transform it to obtain the right side. Choose the correct step and transform the expression according to the step chosen.
secx-1/ tan x= sec-1 / tanx

Answer 1

Proved

Explanation:

The options are not given. So, I will solve from scratch

Given

`(secx-1)/(tan x)= (tanx)/(secx+1)`

Required

Prove

Multiply the right-hand side by
`(secx + 1)/(secx + 1)`

`(secx-1)/(tan x) * (secx + 1)/(secx + 1)= (tanx)/(secx+1)`

Apply difference of two squares on the numerator

`(sec^2 x - 1)/((tanx)(secx + 1)) =(tanx)/(secx+1)`

In trigonometry:

`tan^2x = sec^2x - 1`

So, we have:

`(tan^2 x)/((tanx)(secx + 1)) =(tanx)/(secx+1)`

`(tan x * tan x)/((tanx)(secx + 1)) =(tanx)/(secx+1)`

tan x cancels out

`(tan x)/(secx + 1) =(tanx)/(secx+1)`

Proved