Question

Find the principal value of \( \sin^{-1}\!\left(-\frac{\sqrt{3}}{2}\right) + \cosec^{-1}\left(-\frac{2}{\sqrt{3}}\right). \)\!

Hint:

Use identity: \( \cosec^{-1}x = \sin^{-1}\!\left(\frac{1}{x}\right) \)
and always check principal value ranges.

Answer 1