Question

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

Answer 1

\[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right) = \tan^{- 1} \left( \tan\frac{\pi}{4} \right) + \cos^{- 1} \left( \cos\frac{2\pi}{3} \right)\]
\[ = \frac{\pi}{4} + \frac{2\pi}{3}\]
\[ = \frac{11\pi}{12}\]