Question

The value of ${\cos }^{-1}\left(\cos 12\right)-{\sin }^{-1}\left(\sin 14\right)$ is

• A. $0$
• B. $8\pi -26$
• C. $4\pi +2$
• D. None of these

Answer 1

The correct option is B $8\pi -26$

The value of

${\cos }^{-1}\left(\cos 12\right)-{\sin }^{-1}\left(\sin 14\right)$

$={\cos }^{-1}\left(\cos (4\pi -12)\right)-{\sin }^{-1}(-\sin (4\pi -14))$...................$(\because \sin (-\theta )=-\sin \theta )$

$=4\pi -12-14+4\pi =8\pi -26$