Question

Write as the sine of a single angle:

(1) \(2 \sin 3 \theta \cdot \cos 3 \theta\)

(2) \(2 \sin \frac{\mathrm{A}}{2} \cdot \cos \frac{\mathrm{A}}{2}\)

(3) \(4 \sin x \cos x\)

Answer 1

(1) \(2 \sin 3 \theta \cdot \cos 3 \theta=\sin [2(3 \theta)]=\sin 6 \theta\)

(2) \(2 \sin \frac{\mathrm{A}}{2} \cdot \cos \frac{\mathrm{A}}{2}=\sin \left[2\left(\frac{\mathrm{A}}{2}\right)\right]=\sin \mathrm{A}\)

(3) \(4 \sin x \cos x=2 \times 2 \sin x \cos x=2 \sin 2 x\)
\((4 \sin x \cos x \neq \sin 4 x)\)