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

Explanation

To prove that \( \cot^{-1}\left(\frac{3}{4}\right) + \sin^{-1}\left(\frac{5}{13}\right) = \sin^{-1}\left(\frac{63}{65}\right) \), we will follow these steps:

### Step 1: Define the angles
Let:
\[ \theta = \cot^{-1}\left(\frac{3}{4}\right) \]
This implies that:
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