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Use the compound angle formulae to simplify each expression to one term only:

(a) $\cos 3 \theta \cdot \cos \theta+\sin 3 \theta \cdot \sin \theta$

(b) $\cos 2 x \cdot \cos 3 x-\sin 2 x \cdot \sin 3 x$

(c) $\sin 4 \mathrm{P} \cdot \cos 2 \mathrm{P}-\cos 4 \mathrm{P} \cdot \sin 2 \mathrm{P}$

(d) $\sin 10^{\circ} \cdot \cos 4 \theta+\cos 10^{\circ} \cdot \sin 4 \theta$

(e) $\sin 3 x \cdot \cos x-\cos 3 x \cdot \sin x$

(f) $\cos 2 x \cdot \sin 3 x-\cos 3 x \cdot \sin 2 x$

(g) $\sin 4 \theta \cdot \sin 5 \theta-\cos 5 \theta \cdot \cos 4 \theta$
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