1. ## Trig...Simplifying

How do I simplify this problem (so that the Right Side is equal to the Left Side)?

cosx - (cosx)/(1-tanx) = (sinx cosx)/ (sinx - cosx)

2. Without telling you the entire solution, I will give you some hints. First, change everything into sines and cosines, so the tangent must equal sine/cosine. From there, you can multiply out and see the equality.

3. I am going to post a scan of the work that I did...i think that I might be on the right track, but messed up somewhere...it will just take me a minute to upload...

4. Please ignore 25 continued...underneath it....it is another problem

5. You are right so far except your denominator has disappeared.

It must be:
$\frac{cos x-\frac{sin x cos x}{cosx}-cos x}{1-tan x}$

The numerator can be simplified to
$\frac{cos x-sinx-cos x}{1-tan x}= \frac{-sinx}{1-tan x}$

Then as previously stated change $tan x$ in the denominator to $\frac{sinx}{cos x}$

6. Now I have got:
-sinx/ 1-(sinx/cosx) What do I do now?

7. $-\frac{sin x}{1-\frac{sin x}{cosx}}$

$-\frac{sin x}{\frac{cos x}{cos x}-\frac{sin x}{cos x}}$ Common denominators

$-\frac{sin x}{\frac{cos x - sin x}{cos x}}$

$-sin x \cdot \frac{cos x}{cos x - sin x}$ Multiply the reciprocal

$-\frac{sin x \cdot cos x}{-(sin x - cos x)}$ Simplify the bottom

$\frac{sin x \cdot cos x}{(sin x - cos x)}=RHS$