The value of \left(sin\right)^{- 1} \left(\right. \frac{12}{13} \left.\right) - \left(sin\right)^{- 1} \left(\right. \frac{3}{5} \left.\right) is equal to

Engineering

Mathematics

Properties of Inverse Trigonometric Function

Question

The value of $\sin^{- 1} (\frac{12}{13}) - \sin^{- 1} (\frac{3}{5})$ is equal to

$\frac{π}{2} - \sin^{- 1} (\frac{56}{65})$

$π - \cos^{- 1} (\frac{33}{65})$

$\frac{π}{2} - \cos^{- 1} (\frac{9}{65})$

$π - \sin^{- 1} (\frac{63}{65})$

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$\sin^{- 1} (\frac{12}{13}) - \sin^{- 1} (\frac{3}{5})$

$\sin^{- 1} (x \sqrt{1 - y^{2}} - y \sqrt{1 - x^{2}})$

$= \sin^{- 1} (\frac{33}{65}) = \cos^{- 1} (\frac{56}{65}) = \frac{π}{2} - \sin^{1} (\frac{56}{65})$