Find the Maclaurin expansion for using the double angle identity for cos2x and cos4x.

So...

This is how i worked out so far, yet i'm not sure whether it is correct or not

Identity of cos4x = cos(2x + 2x) = cos2x.cos2x + sin2x.sin2x

using the identity of

which equals to

hence

If it is correct i'm not sure whether to continue with the problem or not, this question has 8 marks...and i'm puzzled.. if anyone could help it would be greatly appreciated!

thanks in advance

kleyzam