Prove that cos-112/13 + sin-1 3/5 …

Let ${\cos ^{ - 1}}\frac{{12}}{{13}} = \theta$ so that $\cos \theta = \frac{{12}}{{13}}$
$\therefore \sin \theta = \sqrt {1 - {{\cos }^2}\theta } = \sqrt {1 - \frac{{144}}{{169}}}$$= \sqrt {\frac{{25}}{{169}}} = \frac{5}{{13}}$
Again, Let ${\sin ^{ - 1}}\frac{3}{5} = \phi$ so that $\sin \phi = \frac{3}{5}$
$\therefore \cos \phi = \sqrt {1 - {{\sin }^2}\phi } = \sqrt {1 - \frac{9}{{25}}} = \sqrt {\frac{{16}}{{25}}} = \frac{4}{5}$
Since $\sin \left( {\theta + \phi } \right) = \sin \theta \cos \phi + \cos \theta \sin \phi$ $= \frac{5}{{13}} \times \frac{4}{5} + \frac{{12}}{{13}} \times \frac{3}{5}$ 
$= \frac{{20 + 36}}{{65}} = \frac{{56}}{{65}}$
$\Rightarrow \theta + \phi = {\sin ^{ - 1}}\frac{{56}}{{65}}$
$\Rightarrow {\cos ^{ - 1}}\frac{{12}}{{13}} + {\sin ^{ - 1}}\frac{3}{5} = {\sin ^{ - 1}}\frac{{56}}{{65}}$