Question

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

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

Answer 1

The correct option is B

$8\mathrm{\pi }-26$

Explanation for correct option

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

$$\begin{gathered} ={\cos }^{-1}\left(\cos \left(4\mathrm{\pi }-12\right)\right)-{\sin }^{-1}\left(-\sin \left(4\mathrm{\pi }-14\right)\right)\left[\because \sin \left(-\theta \right)=-\sin \left(\theta \right)\right] \\ =4\pi -12-14+4\pi \\ =8\pi -26 \end{gathered}$$

Hence, the correct option is $\mathrm{Option}\left(\mathrm{B}\right)$