C and D are complementary angles, so their cofunctions are equal:

$\displaystyle{\tan{{D}}}={\cot{{C}}}=\frac{{8}}{{15}}\usepackage{cmbright}\Huge\$

$\displaystyle{\sin{{C}}}={\cos{{D}}}=\frac{{15}}{{17}}\usepackage{cmbright}\Huge\$