Chứng minh rằng trong tam giác $ABC$, ta có:
a) $\sin A+ \sin B+ \sin C = 4\cos \frac{A}{2} \cos \frac{B}{2}\cos \frac{C}{2} $
b) $\cos A + \cos B + \cos C=1+ 4\sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2} $
c) $\sin 2A+ \sin 2B+ \sin 2C = 4 \sin A \sin B \sin C$
d) $\cos^2 A+\cos^2 B+ \cos^2 C+2\cos A \cos B \cos C =1$
e) $\sin^2 A +\sin^2 B +\sin^2 C = 2(1+\cos A \cos B \cos C) $