Simple Harmonic Motion with Transformations

Prove the following motions are simple harmonic and find the centre of motion, the period and the amplitude.

1. $\displaystyle x=2+cos 3t - \sqrt 3 sin 3t$

With this I tried to put the 2 over to the other side so that it becomes $\displaystyle x-2=cos 3t - \sqrt 3 sin 3t$and transform to $\displaystyle R sin (3t+\alpha)$ but I got stuck at the transformation bit.

2. $\displaystyle x=6 cos^2 8t -4$

First I differentiated and got $\displaystyle 12cos 8t (-sin 8t)$ which is the same as $\displaystyle -12cos 8t sin 8t$ right? And I know I have to differentiate again but do I use product rule or differentiate altogether?