Chứng minh rằng trong tam giác ABC, ta có:

\(\sin \frac{A}{2} = \cos \frac{{B + C}}{2}\);

Ta có: \(\frac{{A + B + C}}{2} = \frac{\pi }{2}\), suy ra \(\frac{{B + C}}{2} = \frac{\pi }{2} - \frac{A}{2}\).

Nên \(\sin \frac{A}{2} = \cos \frac{{B + C}}{2}\).