\( \left.\begin{array}{l}\text { Question } 3 \\ \text { Use the identities for compound angles and simplify } \\ \text { without a calculator. } \\ 3.1 \cos 2 A \cos A-\sin 2 A \sin A \\ 2 \cos A \\ 3.2 \sin 3 \alpha \cos \alpha+\cos 3 \alpha \sin \alpha \\ 1-2 A\end{array}\right) \)

To simplify \( \cos 2A \cos A - \sin 2A \sin A \), we can utilize the cosine of sum formula, which states that \( \cos(x + y) = \cos x \cos y - \sin x \sin y \). By letting \( x = 2A \) and \( y = A \), we find that this expression simplifies to \( \cos(2A + A) = \cos(3A) \). Thus, we have: \[ \cos 2A \cos A - \sin 2A \sin A = \cos(3A). \] Next, for the second expression \( \sin 3\alpha \cos \alpha + \cos 3\alpha \sin \alpha \), we can apply the sine of sum formula, which is \( \sin(x + y) = \sin x \cos y + \cos x \sin y \). Here, letting \( x = 3\alpha \) and \( y = \alpha \), the expression simplifies to: \[ \sin(3\alpha + \alpha) = \sin(4\alpha). \] Therefore, the simplified forms are: 1. \( \cos 2A \cos A - \sin 2A \sin A = \cos(3A) \) 2. \( \sin 3\alpha \cos \alpha + \cos 3\alpha \sin \alpha = \sin(4\alpha). \)