If $$\frac{{\sin \theta + \cos \theta }}{{\sin \theta - \cos \theta }} = 3{\text{,}}$$    then the value of $${\sin ^4}\theta $$   is?

Solution (By Examveda Team)

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