Prove that:`tan^(-1)(63/16)=sin^(-1)(5/13)+cos^(-1)(3/5)`

Explanation

`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

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