`R.H.S -> sin^-1(5/13)+cos^-1(3/5)`
We can create two triangles with angle `theta` and `phi` as expalined in video.
In that case,
`sin^-1(5/13)` can be written as `tan^-1(5/12)`
`cos^-1(3/5)` can be wriiten as `tan^-1(4/3)`
So, we can rewrite R.H.S. as
`tan^-1(5/12)+tan^-1(4/3)`
As, `tan^-1x+tan^-1y = tan^-1((x+y)/(1-xy))`, above can be wtitten as
`tan^-1(5/12+4/3)/(1-5/12**4/3)`
`=tan^-1((7/4)/(4/9)) = tan^-1(63/16) = L.H.S.`