# How to simplify following trignometric expression

1. Jul 26, 2013

### needingtoknow

1. The problem statement, all variables and given/known data

- 1/[cosx(cos(x-90))]

3. The attempt at a solution

= - 1/[cosx(-cos(90-x))] //so first I take the negative sign out from (x-90) to make it (90-x)
= +1/[cosx(cos(90-x))] // negative sign from outside the cos and outside the entire fraction combine to become positive
= 1/[cosx(sinx)] //because cos(x-90) = sinx

However this answer is incorrect the answer in the back states the following:

2. Jul 26, 2013

### Staff: Mentor

$\cos(-x)=\cos(x)$, therefore $\cos(x-90) = \cos(90-x)$.

3. Jul 26, 2013

### needingtoknow

Oh yes that completely slipped my mind. Thank you Dr Claude!

4. Jul 26, 2013

### Ray Vickson

Do you mean $\cos(x) \cos(x-90)?$ If so, write it as cos(x)*cos(x-90), because what you wrote could well mean something else, such as
$$\cos\left( x \cos(x-90)\right)$$
or something similar.

5. Jul 26, 2013

### needingtoknow

Duly noted thanks for the tip!