Question

Write.the principal value of ${\tan }^{-1}1+{\cos }^{-1}\left(-\frac{1}{2}\right)$

Answer 1

$$\begin{gathered} {\tan }^{-1}1+{\cos }^{-1}\left(-\frac{1}{2}\right)={\tan }^{-1}\left(\tan \frac{\mathrm{\pi }}{4}\right)+{\cos }^{-1}\left(\cos \frac{2\mathrm{\pi }}{3}\right) \\ =\frac{\mathrm{\pi }}{4}+\frac{2\mathrm{\pi }}{3} \\ =\frac{11\mathrm{\pi }}{12} \end{gathered}$$