Hello TeriyakiDonnQThe 'double-angle' identities you're referring to tell you how to find the sine and cosine of an angle if you know the sine and cosine of the angle half its size. Here's the one for sine:...(1)So this means, for example, that:

Now if you divide both sides of (1) by 2, you'll get:

... and so on.

Can you see, then, that if , this will give:

With the formula for , there's more than one possibility. You can start with:

but then, if you use the identity (which I'm sure you know), you can write, alternatively:or:

Which one of these three you use depends on the circumstances, but they are all correct.

You are given the expression . Well, that's just the RHS of the second of these three cosine formulae with . (If you simply didn't spot this, that's because you haven't had enough practice yet!)

So, using the second formula with , we get:Grandad