Originally Posted by

**skeeter** since A and B are about to slide, the static friction force is at a maximum, and the system is in equilibrium.

forces on A ...

$\displaystyle

W\sin{\alpha} - T - \mu W\cos{\alpha} = 0

$

forces on B ...

$\displaystyle

T - \mu W\cos{\beta} - W\sin{\beta} = 0

$

combine the equations ...

$\displaystyle

W(\sin{\alpha} - \sin{\beta}) - \mu W(\cos{\alpha} + \cos{\beta}) = 0

$

solving for $\displaystyle \mu$ ...

$\displaystyle

\mu = \frac{\sin{\alpha} - \sin{\beta}}{\cos{\alpha} + \cos{\beta}}

$

I'll leave the identity work for you.