Question

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

• A. $0$
• B. $\pi$
• C. $8\pi +24$
• D. $8\pi -24$

Answer 1

The correct option is A $0$

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

$={\cos }^{-1}\sqrt{1-{\sin }^{2}12}-{\cos }^{-1}\left(\cos 12\right)$ since ${\sin }^{-1}x={\cos }^{-1}\sqrt{1-x^2}$

$={\cos }^{-1}\left(\cos 12\right)-{\cos }^{-1}\left(\cos 12\right)=0$