question_answer

If \[\mathbf{sin}\theta \text{ }+\text{ }\mathbf{cos}\text{ }\theta =\text{ }\mathbf{p}\], then the value of \[\mathbf{si}{{\mathbf{n}}^{\mathbf{6}}}\theta \mathbf{+co}{{\mathbf{s}}^{\mathbf{6}}}\theta \] equals to _________

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

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

C)  \[4-3\left( {{p}^{2}}-1 \right)~~~~~~~~~~~~~~~~~\]                           

D)  \[4-3{{\left( {{p}^{2}}-1 \right)}^{2}}\]

E)  None of these