# Show this simple trigonometric identity add up to 0

Gold Member

## Homework Statement

$$\cos (\frac{(-1)\pi x}{L})-\cos (\frac{3\pi x}{L})$$

## The Attempt at a Solution

the first cosine is the same as positive but is the second cosine simply equal to
$$\cos (\frac{\pi x}{L})$$?

thanks!

verty
Homework Helper
When x = 1, L = 3, we have:

cos(-pi/3) - cos(pi)
= 1 + cos(-pi/3) > 0

Mentallic
Homework Helper
$$\cos(-x)=\cos(x)$$
and
$$\cos(3x)=4\cos^3(x)-3\cos(x)$$

So obviously this isn't going to be equal to 0 for all x.