In a triangle $ABC,C=90^{\circ}$.Then $\large\frac{a^2-b^2}{a^2+b^2}=$

Question

\[\begin {array} {1 1} (1)\;\sin (A+B) & \quad (2)\;\sin (A-B) \\ (3)\;\cos (A+B) & \quad (4)\;\cos (A-B) \end {array}\]