How do I prove the Identity?

Question

 (cotx-1)/(cotx+1)=(1-tanx)/(1+tanx)

Answer 1

In order to do this one, you need to rewrite cot x in terms of tan x and you don't need to touch the right side of the equation.

 

Left side should look like this:

 

(1/tan x - 1)/(1/tan x + 1)

 

Now you need to get a common denominator, which happens to be tan x.  So, if you multiply everything by tan x, you get:

 

(1 - tan x) / (1 + tan x)

 

That looks just like the right side of the equation, so you have proven this identity.