question_answer

The greatest and the least value of \[{{({{\sin }^{-1}}x)}^{3}}+{{({{\cos }^{-1}}x)}^{3}}\] are

A)  \[\frac{-\pi }{2},\]\[\frac{\pi }{2}\]                     

B)  \[\frac{-{{\pi }^{3}}}{8},\]\[\frac{{{\pi }^{3}}}{8}\]

C)  \[\frac{7{{\pi }^{3}}}{8},\]\[\frac{{{\pi }^{3}}}{32}\]

D)  \[\frac{9{{\pi }^{2}}}{16},\]\[\frac{3{{\pi }^{2}}}{4}\]

E)  None of these