A and B are complementary angles, so their cofunctions are equal.

$\displaystyle{\cos{{B}}}={\sin{{A}}}=\frac{{5}}{{13}}\usepackage{cmbright}\Huge\$

$\displaystyle{\csc{{B}}}={\sec{{A}}}=\frac{{13}}{{12}}\usepackage{cmbright}\Huge\$