exo7 3905

Résoudre les équations suivantes :

1

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

2

\(\sin\theta + \sin2\theta + \sin3\theta + \sin4\theta = 0\).

3

\(\cos\theta + \cos2\theta + \cos3\theta = 0\).

4

\(\cos\theta - \cos2\theta = \sin3\theta\).

5

\(\cos\theta + \cos7\theta = \cos4\theta\).

6

\(\cos2\theta + \cos12\theta = \sqrt3\cos5\theta\).

7

\(\sin7\theta - \sin\theta = \sin3\theta\).

8

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

9

\(\sin\theta\sin3\theta = \sin5\theta\sin7\theta\).

10

\(3\tan\theta = 2\cos\theta\).

11

\(\tan4\theta = 4\tan\theta\).

12

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

13

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