Question

Write the value of cos⁻¹ (cos 1540°).

Answer 1

We know that
${\cos }^{-1}\left(\cos x\right)=x$
Now,
$$\begin{gathered} {\cos }^{-1}\left(\cos {1540}^{\circ }\right)={\cos }^{-1}\left\{\cos \left(1440+{100}^{\circ }\right)\right\} \\ ={\cos }^{-1}\left\{\cos \left({100}^{\circ }\right)\right\}\left[\because \cos \left(4\mathrm{\pi }+{100}^{\circ }\right)=\cos 100°\right] \\ ={100}^{\circ } \end{gathered}$$