If $$x\sin {45^ \circ }$$ = $$y\operatorname{cosec} {30^ \circ },$$ then $$\frac{{{x^4}}}{{{y^4}}}$$ is equal to?
A. 43
B. 63
C. 23
D. 83
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & x\sin {45^ \circ } = y\operatorname{cosec} {30^ \circ } \cr & \Rightarrow \frac{x}{y} = \frac{{{\text{cosec 3}}{{\text{0}}^ \circ }}}{{{\text{sin }}{{45}^ \circ }}} \cr & \Rightarrow \frac{x}{y} = \frac{2}{{\frac{1}{{\sqrt 2 }}}} \cr & \Rightarrow \frac{x}{y} = \frac{{2\sqrt 2 }}{1} \cr & \Rightarrow \frac{{{x^4}}}{{{y^4}}} = {\left( {\frac{{2\sqrt 2 }}{1}} \right)^4} \cr & \Rightarrow \frac{{{x^4}}}{{{y^4}}} = \frac{{64}}{1} \cr & \Rightarrow \frac{{{x^4}}}{{{y^4}}} = {4^3} \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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