Express each of the following as the product of sines and cosines: `cos 12theta-cos4theta`

Explanation

`cos 12 theta-cos 4 theta`

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

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

`=-2 sin 8 theta sin 4 theta`