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

Explanation

To prove that \( \tan^{-1}\left(\frac{63}{16}\right) = \sin^{-1}\left(\frac{5}{13}\right) + \cos^{-1}\left(\frac{3}{5}\right) \), we will follow these steps:

### Step 1: Define the angles
Let \( \theta = \sin^{-1}\left(\frac{5}{13}\right) \) and \( \alpha = \cos^{-1}\left(\frac{3}{5}\right) \).

### Step 2: Find \( \cos \theta \)
Using the identity \( \sin^2 \theta + \cos^2 \theta = 1 \):
\[
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