Prove that `cot^(-1).(3)/(4) + sin^(-1).(5)/(13) = sin^(-1).(63)/(65)`

Explanation

`cot^(-1).(3)/(4) + sin^(-1).(5)/(13) = sin^(-1).(4)/(5) + sin^(-1).(5)/(13)`
`=sin^(-1) ((4)/(5) sqrt(1- ((5)/(13))^(2)) + (5)/(3) sqrt(1 - ((4)/(5))^(2)))`
`= sin^(-1) ((4)/(5) (12)/(13) + (5)/(13) (3)/(5)) = sin^(-1).(63)/(65)`