​$$\sin^{-1}\left(\frac{4}{5}\right) - \sin^{-1}\left(\frac{5}{13}\right) = \, ?$$​​

Correct option is B

​$$\text{We can use the subtraction formula for inverse sine:} \\\sin^{-1} A - \sin^{-1} B = \sin^{-1} \left( \left( A \sqrt{1 - B^2} - B \sqrt{1 - A^2} \right) \right) \\\textbf{Identify A and B} \\A = \frac{4}{5}, \quad B = \frac{5}{13} \\\textbf{Compute } \sqrt{1 - A^2} \text{ and } \sqrt{1 - B^2} \\\sqrt{1 - A^2} = \sqrt{1 - \left( \frac{4}{5} \right)^2} = \sqrt{1 - \frac{16}{25}} = \sqrt{\frac{9}{25}} = \frac{3}{5} \\\sqrt{1 - B^2} = \sqrt{1 - \left( \frac{5}{13} \right)^2} = \sqrt{1 - \frac{25}{169}} = \sqrt{\frac{144}{169}} = \frac{12}{13} \\\textbf{Apply the subtraction formula} \\\sin^{-1} \left( \frac{4}{5} \right) - \sin^{-1} \left( \frac{5}{13} \right) = \sin^{-1} \left( \frac{4}{5} \cdot \frac{12}{13} - \frac{5}{13} \cdot \frac{3}{5} \right) \\= \sin^{-1} \left( \frac{48}{65} - \frac{15}{65} \right) = \sin^{-1} \left( \frac{33}{65} \right)$$​​