# Laplace-table cos^2

1. Dec 9, 2004

### TSN79

Does anyone know how to convert

$$cos^2 (2t)$$

into a form that I can use the Laplace-table on...?

2. Dec 9, 2004

### Tide

How about using some trig identities:

$$\cos^2 2x = \frac {1 + \cos 4x}{2}$$

3. Dec 9, 2004

### TSN79

Hey thanks Tide! Just one thing, I wasn't really able to find this identity anywhere in my books, and I'm not really at a level where I can come up with such identities on my own if it goes beyond turning equations around. This identity is not one of the most used is it?

4. Dec 9, 2004

### Tide

TSN,

It's just a variant of the sum formula which is very commonly used:

$$\cos a + b = \cos a \cos b - \sin a \sin b$$

so that when a = b

$$\cos 2a = \cos^2 a - \sin^2 a$$

and since

$$\sin^2 a + \cos^2 a = 1$$

the identity becomes

$$\cos 2a = 2 \cos^2 a - 1$$

from which

$$\cos^2 a = \frac {1 + \cos 2a}{2}$$

Finally, just set a = 2x for your problem.

5. Dec 9, 2004