Question

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

• A. $\pi-\sin^{-1} \left(\frac{63}{65}\right) $
• B. $\pi-\cos^{-1} \left(\frac{33}{65}\right) $
• C. $\frac{\pi}{2} - \sin^{-1} \left(\frac{56}{65}\right) $
• D. $\frac{\pi}{2} -\cos^{-1} \left(\frac{9}{65}\right) $

Answer 1

Answer: (C)

$\sin^{-1} \left(\frac{12}{13}\right) -\sin^{-1} \left(\frac{3}{5}\right) $
$ \sin^{-1} \left(x\sqrt{1-y^{2}} - y\sqrt{1-x^{2}}\right) $
$=\sin^{1} \left(\frac{33}{65} \right) =\cos^{-1} \left(\frac{56}{65} \right) =\frac{\pi}{2} -\sin^{1}\left(\frac{56}{65}\right) $