Question

Write the principal value of : [ cos-1 √3/2 + cos-1 (-1/2) ] .

Answer 1

We know that ,
$\cos {}^{ - 1} \binom{ \sqrt{3} }{2} = \ \cos {}^{ - 1} ( \cos( \frac{\pi}{6} ) )$
$\cos {}^{ - 1} \binom{ - 1}{2} = \cos {}^{ - 1} ( \cos(\pi - \frac{\pi}{3} ) )$
Therefore, answer of the following question will be:
$\cos {}^{ - 1} \binom{ \sqrt{3} }{2} + \cos {}^{ - 1} \binom{ - 1}{2} = \frac{5\pi}{6}$