Solve the trigonometric equation:
$$\cos (3x)-\sin(x)=\sqrt 3(\cos (x)-\sin(3x))$$
My answer is contradictory to Wolfram Alpha.
Because, W.A. gives me:
$x = \pi n - \frac {11 \pi}{12}, n \in \mathbb{ Z}$
$x = \pi n - \frac {7 \pi}{12}, n \in \mathbb{ Z}$
$x = \pi n - \frac {3 \pi}{12}, n \in \mathbb{ Z}$
But, my answer is:
$x=\frac {\pi}{12}+\pi k, k\in\mathbb{Z}$
$x=\frac {\pi}{8}+\frac {\pi k}{2}, k\in\mathbb{Z}$
Is my solution wrong? Or What is the problem in my solution?