# Thread: [SOLVED] What is the identity used here?

1. ## [SOLVED] What is the identity used here?

This is part of a larger example problem that I came across in reviewing. I can't for the life of me remember the identity or principle that would get one from the first form to the second in one step. Maybe it is not one step -- the authors of the textbook eliminated what they assumed one would see automatically? I realize this may be a stupid question, but it is driving me crazy. Anyone?

$\displaystyle \cos{(\pi-2\theta)} = \frac{20-x}{x}$

$\displaystyle \cos{(2\theta)} = \frac{x-20}{x}$

2. Hello sinewave85
Originally Posted by sinewave85
This is part of a larger example problem that I came across in reviewing. I can't for the life of me remember the identity or principle that would get one from the first form to the second in one step. Maybe it is not one step -- the authors of the textbook eliminated what they assumed one would see automatically? I realize this may be a stupid question, but it is driving me crazy. Anyone?

$\displaystyle \cos{(\pi-2\theta)} = \frac{20-x}{x}$

$\displaystyle \cos{(2\theta)} = \frac{x-20}{x}$
For any angle $\displaystyle \theta, \cos(\pi-\theta) =-\cos(\theta)$

So $\displaystyle \cos(\pi-2\theta) = \frac{20-x}{x}$

$\displaystyle \Rightarrow -\cos(2\theta) = \frac{20-x}{x}$

$\displaystyle \Rightarrow\cos(2\theta) = -\frac{20-x}{x} = \frac{x-20}{x}$

For any angle $\displaystyle \theta, \cos(\pi-\theta) =-\cos(\theta)$