Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

${\sin }^{-1}\left(\frac{12}{13}\right)-{\sin }^{-1}\left(\frac{3}{5}\right)$
$={\tan }^{-1}\left(\frac{12}{5}\right)-{\tan }^{-1}\left(\frac{3}{4}\right)$$\left[{\sin }^{-1}x={\tan }^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right)\right]$
$={\tan }^{-1}\left(\frac{\frac{12}{5}-\frac{3}{4}}{1+\frac{12\times 3}{5\times 4}}\right)$
$={\tan }^{-1}\left(\frac{33}{56}\right)$
$={\sin }^{-1}\left(\frac{33}{65}\right)$
$={\cos }^{-1}\left(\frac{56}{65}\right)=\frac{\pi }{2}-{\sin }^{-1}\left(\frac{56}{65}\right)$