Exercices corrigés
| Exercice 1. Transformer {\cos x+2\cos 2x+\cos3x} en produit. |
| Exercice 2. Transformer {S=\sin x+\sin2x+\sin7x+\sin8x} en produit. |
| Exercice 3. Simplifier la somme {S= \displaystyle\sum_{k=1}^n\cos\bigl((2k-1)\theta\bigr)}. |
| Exercice 4. Simplifier la somme {S= \displaystyle\sum_{k=0}^n\cos^2(k\theta)}. |
| Exercice 5. Montrer que: {\forall\,a\in \mathbb{R}}, {\forall\,h\in\,]0,\pi[}, {\forall\,n\in \mathbb{N}^*}, {\displaystyle\sum_{k=0}^{n-1}\cos(a\!+\!2kh)\!=\!\dfrac{\sin(nh)\cos(a\!+\!(n\!-\!1)h)}{\sin h}} |