Soit \(\theta \in \R\).
1
Simplifier \(\cos^4\theta + \cos^4\left(\theta + \frac \pi4\right) + \cos^4\left(\theta + \frac {2\pi}4\right) + \cos^4\left(\theta + \frac {3\pi}4\right)\).
2
Simplifier \(\cos^6\theta + \cos^6\left(\theta + \frac \pi6\right) + \dots + \cos^6\left(\theta + \frac {5\pi}6\right)\).
3
Simplifier \(\cos^{2p}\theta + \cos^{2p}\left(\theta + \frac \pi{2p}\right) + \dots + \cos^{2p}\left(\theta + \frac {(2p-1)\pi}{2p}\right)\).