Express each of the following as the product of sines and cosines: `sin 12theta+sin4theta`

Explanation

`sin 12 theta+sin 4 theta`

`=2 sin (frac{12 theta+4 theta}{2}) cos (frac{12 theta-4 theta}{2})`

`{therefore sin A+sin B=2 sin (frac{A+B}{2}) cos (frac{A-B}{2})}`

`=2 sin 8 theta cos 4 theta`