# Proving identitiees

• Oct 20th 2009, 12:57 AM
reiward
Proving identitiees
$\displaystyle \frac{sec x + 1}{tan x} = \frac{tan x}{sec x -1}$

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

Thank you.!
• Oct 20th 2009, 02:25 AM
mr fantastic
Quote:

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

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

Thank you.!

Substitute $\displaystyle \tan x = \frac{\sin x}{\cos x}$ and $\displaystyle \sec x = \frac{1}{\cos x}$ and simplify:

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

RHS $\displaystyle = \frac{\sin x}{1 - \cos x} = \frac{\sin x}{(1 - \cos x)} \cdot \frac{(1 + \cos x)}{(1 + \cos x)} = \frac{\sin x (1 + \cos x)}{(1 - \cos^2 x)}$ and it should be clear how to continue and end up with the LHS.
• Oct 20th 2009, 02:35 AM
reiward
Quote:

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

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

RHS $\displaystyle = \frac{\sin x}{1 - \cos x} = \frac{\sin x}{(1 - \cos x)} \cdot \frac{(1 + \cos x)}{(1 + \cos x)} = \frac{\sin x (1 + \cos x)}{(1 - \cos^2 x)}$ 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 $\displaystyle \frac{sec x + 1}{tan x} = \frac{sec x + 1}{tan x}$

So from the LHS, can you show me how to make the LHS into $\displaystyle \frac{sec x + 1}{tan x}$
• Oct 20th 2009, 02:45 AM
mr fantastic
Quote:

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

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

Divide numerator and denominator by $\displaystyle \cos x$.