L3 calculus:
simplify the trigonometric expression:

3

5cos^3(pi/3)

would be greatly appreciated, step by step. xx

so you have

###

If you don't remember the value of off the top of your head, it's possible to derive it with some identities and knowing that .

Consider the expression . With the angle sum identity, we have

and the double angle identities give

Write everything in terms of cosine:

Now let . Then

Let . Then

The rational root theorem suggests some possible roots are

and checking all of these, we find that is among the solution set. In fact,

We have only for odd multiples of , so it follows that