If $$x\sin {45^ \circ }$$  = $$y\operatorname{cosec} {30^ \circ },$$   then $$\frac{{{x^4}}}{{{y^4}}}$$  is equal to?

$$\eqalign{ & x\sin {45^ \circ } = y\operatorname{cosec} {30^ \circ } \cr & \Rightarrow \frac{x}{y} = \frac{{{\text{cosec 3}}{{\text{0}}^ \circ }}}{{{\text{sin }}{{45}^ \circ }}} \cr & \Rightarrow \frac{x}{y} = \frac{2}{{\frac{1}{{\sqrt 2 }}}} \cr & \Rightarrow \frac{x}{y} = \frac{{2\sqrt 2 }}{1} \cr & \Rightarrow \frac{{{x^4}}}{{{y^4}}} = {\left( {\frac{{2\sqrt 2 }}{1}} \right)^4} \cr & \Rightarrow \frac{{{x^4}}}{{{y^4}}} = \frac{{64}}{1} \cr & \Rightarrow \frac{{{x^4}}}{{{y^4}}} = {4^3} \cr} $$