If + - = 3 , then the value of ^4 is?

Answer: Option A

\begin{aligned} & \frac{{\sin \theta + \cos \theta }}{{\sin \theta - \cos \theta }} = \frac{3}{1} \\ & {\text{Find }}{\sin ^4}\theta = ? \\ & \frac{{\sin \theta + \cos \theta }}{{\sin \theta - \cos \theta }} = \frac{3}{1} \\ & \left( {{\text{by C & D}}} \right) \\ & \Rightarrow \frac{{\sin \theta }}{{\cos \theta }} = \frac{{3 + 1}}{{3 - 1}} \\ & \Rightarrow {\text{tan}}\theta = 2 \\ & {\text{tan}}\theta = \frac{{{\text{Perpendicular}}}}{{{\text{Base}}}} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{2}{1} \\ & \Rightarrow {\sin ^4}\theta \Rightarrow {\left( {\frac{2}{{\sqrt 5 }}} \right)^4} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{16}}{{25}} \\\end{aligned}