Prove the following results: `tan(sin^(-1)(5)/(13)+cos^(-1)3/5)=(63)/(16)` (ii) `sin(cos^(-1)3/5+sin^(-1)5/(13))=(63)/(65)`

Options

A. `48/65`
B. `15/65`
C. `33/65`
D. `63/65`

Explanation

To prove the given results, we will break down each part step by step.

### Part (i): Prove that \( \tan\left(\sin^{-1}\left(\frac{5}{13}\right) + \cos^{-1}\left(\frac{3}{5}\right)\right) = \frac{63}{16} \)

**Step 1: Let \( \theta = \sin^{-1}\left(\frac{5}{13}\right) \)**
This means that \( \sin \theta = \frac{5}{13} \).

**Hint:** Recall that \( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} \).
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