Sine and Cosine equation ( diophantine ) $\cos(\frac{1}{ab} \pi) = \sin(\frac{a}{b} \pi)$
Let $a$ and $b$ be positive integers. What is the full set of solutions?
An example is $a = 2$ and $b = 5$.
I assume the best method is to take $\arccos$ on both sides and solve the resulting diophantine equation?

Thanks to the hint given i can solve the question easily now.
$a = 1$ is trivial.
So Lets take $a <> 1$.
Using $cos(x) = sin(1/2 \pi - x)$ we get
$\frac{1}{2} + \frac{-1}{ab} = \frac{a}{b} + 2k$
$\frac{ab}{2ab} + \frac{-2}{2ab} = \frac{(2aa+4kab)}{2ab}$
$ab - 2 = 2aa + 4kab$
$2aa + (4k-1)ab = -2$
$a(2a + (4k-1)b) = -2$
$a=2$
$4+(4k-1)b = -1$
$(4k-1)b = -5$
$b=5$
Thanks for the help.  I cant believe i missed the evident.
