53.1k views
2 votes
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

User Saurabh
by
6.8k points

1 Answer

6 votes

Answer:

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

User Hedy
by
7.3k points