Bonsoir,
1) Calculer :
[tex]\frac{\pi}{3} - \frac{\pi}{4} = \frac{4\pi}{12} - \frac{3\pi}{12} = \frac{\pi}{12}[/tex]
2) en déduire :
[tex]cos(\frac{\pi}{12}) = cos((\frac{\pi}{3} - \frac{\pi}{4})[/tex]
[tex]cos(\frac{\pi}{12}) = cos(\frac{\pi}{3}).cos(\frac{\pi}{4}) + sin(\frac{\pi}{3}).sin(\frac{\pi}{4})[/tex]
[tex]cos(\frac{\pi}{12}) = \frac{1}{2} \times \frac{\sqrt2}{2} + \frac{\sqrt3}{2} \times \frac{\sqrt2}{2}[/tex]
[tex]cos(\frac{\pi}{12}) = \frac{\sqrt2}{4} + \frac{\sqrt6}{4}[/tex]
[tex]cos(\frac{\pi}{12}) = \frac{\sqrt6 + \sqrt2}{4}[/tex]
