Question

Find the value of ${\cos }^{-1}\left(\cos 12\right)-{\sin }^{-1}\left(\sin 12\right)$

Answer 1

Let $P={\cos }^{-1}\left(\cos 12\right)-{\sin }^{-1}\left(\sin 12\right)$

$={\cos }^{-1}\left(\cos (4\pi -12)\right)-{\sin }^{-1}\left(\sin (12-4\pi )\right)$

$=4\pi -12-(12-4\pi )$

$=4\pi -12-12+4\pi =8\pi -24$