Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

${\mathrm{Cos}}^{-1}\mathrm{Cos}(12)-{\mathrm{Sin}}^{-1}(\mathrm{Sin}12)=(4\pi -12)-(12-4\pi )=8\pi -24$.

The range of ${\mathrm{Cos}}^{-1}$ is $[0,\pi ]$ and ${\mathrm{Sin}}^{-1}$ is $[-\frac{\pi }{2},\frac{\pi }{2}]$.