Prove that:`sin^(-1)(8/17)+sin^(-1)(3/5)=tan^(-1)(77/36)`

Explanation

To prove that \( \sin^{-1}\left(\frac{8}{17}\right) + \sin^{-1}\left(\frac{3}{5}\right) = \tan^{-1}\left(\frac{77}{36}\right) \), we will convert the sine inverse terms into tangent inverse terms and then use the tangent addition formula.

### Step 1: Convert \( \sin^{-1}\left(\frac{8}{17}\right) \) to \( \tan^{-1} \)

Let \( \theta = \sin^{-1}\left(\frac{8}{17}\right) \).

From the definition of sine, we have:
\[
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