Trigonometric Ratios And Identities

If $\tan \alpha=\frac{-12}{5}, \cot \beta=\frac{7}{24}, \alpha$ does not belong to second quadrant and $\beta$ does not belong to first quadrant, then $\sqrt{13} \sin \frac{\alpha}{2}+\cos \frac{\beta}{2}+\tan \frac{\alpha}{2} \cot \frac{\beta}{2}=$