question_answer

If \[\sin \theta +\cos \theta =p,\] then the value of \[{{\sin }^{6}}\theta +{{\cos }^{6}}\theta \] equals to ______.

A)  \[\frac{4+3\,({{p}^{2}}-1)}{4}\]                     

B)  \[\frac{4-3\,{{({{p}^{2}}-1)}^{2}}}{4}\]

C)  \[\frac{4-3\,({{p}^{2}}-1)}{4}\]                       

D)  \[\frac{4+3\,({{p}^{2}}-1)}{4}\]

E)  None of these