# But I See Two Variables!

Calculus Level pending

$\large \int_0^{\pi/6}\dfrac{\cos 2x-\cos 2\beta}{\cos x - \cos\beta}\, d\beta=\dfrac{A\pi}B\cos x+A$

Let $$x$$ be a constant real number such that $$\cos x - \cos\beta \ne 0$$ for $$0 \leq \beta \leq \dfrac\pi 6$$.

If the above equation is true for integers $$A$$ and $$B$$, then find $$2(A+B)$$.

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