<s>[INST] Trigonometry equation, odd-function. So I have the following equation:
$\sin\left(x-\frac{\pi}{6}\right) + \cos\left(x+\frac{\pi}{4}\right)=0$
It should be solved using the fact that Sin is an odd function, I can not really get the gripp of how and what I need to do? Any sugestions?
 [/INST] So i found the solution using the fact that Sin is odd, here is my solution:
$\sin\left (x-\frac{\pi}{6}\right ) + \cos\left (x+\frac{\pi}{4}\right ) = 0\Leftrightarrow \cos\left (x+\frac{\pi}{4}\right ) = -\sin\left (x-\frac{\pi}{6}\right )$ 
Since sin is an odd function, $-\sin\left (x-\frac{\pi}{6}\right ) = \sin\left (x-\frac{\pi}{6} + \pi\right )$ 
This the gives the following:
$\cos\left (x+\frac{\pi}{4}\right ) = \sin\left (x-\frac{\pi}{6} + \pi\right ))\Leftrightarrow \cos\left (x+\frac{\pi}{4}\right ) = \cos\left (\frac{\pi}{2} -\frac{5\pi}{6} -x\right )$
This happends when:
$x + \frac{\pi}{4} = \frac{-2\pi}{6}-x+n2\pi \Leftrightarrow x=\frac{-7\pi}{24}+n\pi$
Thanks alot for the help, special thanx to @BLAZE, you gave me the hints to find the solution. 
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