Question

Express sin 12 theta + sin 4 theta as the product of sines and cosines.

Answer 1

$$\begin{gathered} \sin 12\mathrm{\theta }+\sin 4\mathrm{\theta } \\ =2\sin \left(\frac{12\mathrm{\theta }+4\mathrm{\theta }}{2}\right)\cos \left(\frac{12\mathrm{\theta }-4\mathrm{\theta }}{2}\right) \\ =2\sin 8\mathrm{\theta cos}4\mathrm{\theta } \\ \mathrm{Using}\mathrm{the}\mathrm{formula}\mathrm{sinC}+\mathrm{sinD}=2\sin \left(\frac{\mathrm{C}+\mathrm{D}}{2}\right)\cos \left(\frac{\mathrm{C}-\mathrm{D}}{2}\right) \end{gathered}$$