Prove that: `sin^(-1)(4/5)+sin^(-1)(5/(13))+sin^(-1)((16)/(65))=pi/2`

Explanation

To prove that \( \sin^{-1}\left(\frac{4}{5}\right) + \sin^{-1}\left(\frac{5}{13}\right) + \sin^{-1}\left(\frac{16}{65}\right) = \frac{\pi}{2} \), we will follow these steps:

### Step 1: Combine the first two terms
We start with the left-hand side (LHS):
\[ \sin^{-1}\left(\frac{4}{5}\right) + \sin^{-1}\left(\frac{5}{13}\right) \]
Using the formula for the sum of inverse sines:
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