Given that \(\mathrm{f}(x)=7\cos^2x-3\sin^2x\), where \(0\le x\le\pi\),
express \(\mathrm{f}(x)\) in the form of \(a\cos2x+b\), where \(a\) and \(b\) are constants,[3]
state the greatest and least values of \(\mathrm{f}(x)\),[2]
state the period and amplitude of \(\mathrm{f}(x)\).[2]
Sketch the graph of \(y=\mathrm{f}(x)\) for \(0\le x\le\pi\).[2]