(i) Find the maximum and minimum values of `sin^(4)x + cos^(2)x` and hence or otherwise find the maximum value of `sin^(1000)x + cos^(2008)x`.
(ii) Find the maximum value of cos (cos x).

Explanation

To solve the given problems step by step, we will tackle each part separately.

### Part (i): Find the maximum and minimum values of \( \sin^4 x + \cos^2 x \)

1. **Rewrite the expression**:
We start with the expression \( \sin^4 x + \cos^2 x \). We can express \( \sin^4 x \) in terms of \( \cos^2 x \):
\[
\sin^4 x = (\sin^2 x)^2 = (1 - \cos^2 x)^2
...