Express each of the following as the product of sines and cosines: `sin2theta+cos4theta`

Explanation

`sin 2 theta+cos 4 theta`

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

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

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

`=2 sin (frac{pi}{4}-theta) cos (3 theta-frac{pi}{4})`