# Math Help - Proving identitiees

1. ## Proving identitiees

$\frac{sec x + 1}{tan x} = \frac{tan x}{sec x -1}$

x there is θ. I don't know how to put the θ.

Thank you.!

2. Originally Posted by reiward
$\frac{sec x + 1}{tan x} = \frac{tan x}{sec x -1}$

x there is θ. I don't know how to put the θ.

Thank you.!
Substitute $\tan x = \frac{\sin x}{\cos x}$ and $\sec x = \frac{1}{\cos x}$ and simplify:

LHS $= \frac{1 + \cos x}{\sin x}$

RHS $= \frac{\sin x}{1 - \cos x} = \frac{\sin x}{(1 - \cos x)} \cdot \frac{(1 + \cos x)}{(1 + \cos x)} = \frac{\sin x (1 + \cos x)}{(1 - \cos^2 x)}$ and it should be clear how to continue and end up with the LHS.

3. Originally Posted by mr fantastic
Substitute $\tan x = \frac{\sin x}{\cos x}$ and $\sec x = \frac{1}{\cos x}$ and simplify:

LHS $= \frac{1 + \cos x}{\sin x}$

RHS $= \frac{\sin x}{1 - \cos x} = \frac{\sin x}{(1 - \cos x)} \cdot \frac{(1 + \cos x)}{(1 + \cos x)} = \frac{\sin x (1 + \cos x)}{(1 - \cos^2 x)}$ and it should be clear how to continue and end up with the LHS.
Pardon me, but what is LHS and RHS?

OK, so I get the process of ending up with the LHS you were saying. But in our class, we need to retain the original term of the left or right side. So I need to show that $\frac{sec x + 1}{tan x} = \frac{sec x + 1}{tan x}
$

So from the LHS, can you show me how to make the LHS into $\frac{sec x + 1}{tan x}$

4. Originally Posted by reiward
Pardon me, but what is LHS and RHS?

OK, so I get the process of ending up with the LHS you were saying. But in our class, we need to retain the original term of the left or right side. So I need to show that $\frac{sec x + 1}{tan x} = \frac{sec x + 1}{tan x}
$

So from the LHS, can you show me how to make the LHS into $\frac{sec x + 1}{tan x}$
Divide numerator and denominator by $\cos x$.