(i) Express \(\cos 4\theta\) as \(2 \cos^2 2\theta - 1\) or \(\cos^2 2\theta - \sin^2 2\theta\) or \(1 - 2 \sin^2 2\theta\).

Express \(\cos 4\theta\) in terms of \(\cos \theta\).

Obtain \(8 \cos^4 \theta - 8 \cos^2 \theta + 1\).

Use \(\cos 2\theta = 2 \cos^2 \theta - 1\) to obtain given answer \(8 \cos^4 \theta - 3\).

(ii) (a) State or imply \(\cos^4 \theta = \frac{1}{2}\).

Obtain \(0.572\).

Obtain \(-0.572\).

(b) Integrate and obtain form \(k_1 \theta + k_2 \sin 4\theta + k_3 \sin 2\theta\).

Obtain \(\frac{3}{8} \theta + \frac{1}{32} \sin 4\theta + \frac{1}{4} \sin 2\theta\).

Obtain \(\frac{3}{32}\pi + \frac{1}{4}\) following completely correct work.