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 start from the right-hand side and manipulate it to obtain the left-hand side.

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

### Step 2: Find the tangent of the angles
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