Convert cos^2 (2t) into Laplace Table Form

[TSN79]

Does anyone know how to convert

$$cos^2 (2t)$$

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

 

[Tide]

How about using some trig identities:

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

 

[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?

 

[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.

 

[Astronuc]

For trigonometric identities, try:

http://mathworld.wolfram.com/TrigonometricAdditionFormulas.html