exo7 3905

$(\sqrt6 + \sqrt2)\cos\theta + (\sqrt6 - \sqrt2)\sin\theta = 2$.

$\sin\theta + \sin2\theta + \sin3\theta + \sin4\theta = 0$.

$\cos\theta + \cos2\theta + \cos3\theta = 0$.

$\cos\theta - \cos2\theta = \sin3\theta$.

$\cos\theta + \cos7\theta = \cos4\theta$.

$\cos2\theta + \cos12\theta = \sqrt3\cos5\theta$.

$\sin7\theta - \sin\theta = \sin3\theta$.

$\cos^3\theta\sin3\theta + \cos3\theta\sin^3\theta = \frac 34$.

$\sin\theta\sin3\theta = \sin5\theta\sin7\theta$.

$3\tan\theta = 2\cos\theta$.

$\tan4\theta = 4\tan\theta$.

$\mathrm{cotan}\theta - \tan\theta = \cos\theta + \sin\theta$.

$\begin{cases}\tan x + \tan y = 1\cr \tan(x+y) = 4/3.\end{cases}$