Trigonometric Ratios And Identities

$4 \sin \left(\frac{A+B}{4}\right) \sin \left(\frac{A+C}{4}\right) \sin \left(\frac{A+D}{4}\right)$

$4 \sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A+C}{4}\right) \cos \left(\frac{A+D}{4}\right)$

$4 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A+C}{2}\right) \sin \left(\frac{A+D}{2}\right)$

$4 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A+C}{4}\right) \sin \left(\frac{A+D}{4}\right)$