Question

Use the double angle formulae of sine to expand the following:

(1) \(\sin 4 \mathrm{~A}\)

(2) \(\sin 50^{\circ}\)

(3) \(\sin \mathrm{A}\)

Answer 1

(1) \(\sin 4 \mathrm{~A}=\sin [2(2 \mathrm{~A})]\)

(2) \(\sin 50^{\circ}=\sin \left[2\left(25^{\circ}\right)\right]\)
\[
\therefore \sin 4 \mathrm{~A}=2 \sin 2 \mathrm{~A} \cdot \cos 2 \mathrm{~A} \quad \therefore \sin 50^{\circ}=2 \sin 25^{\circ} \cdot \cos 25^{\circ}
\]

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