If x sin 45^{circ} = y operatorname{cosec} 30 | vedclass

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Question

(A) Given the equation: $x \sin 45^{\circ} = y \operatorname{cosec} 30^{\circ}$.Substitute the trigonometric values: $\sin 45^{\circ} = \frac{1}{\sqrt

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) Given the equation: $x \sin 45^{\circ} = y \operatorname{cosec} 30^{\circ}$.Substitute the trigonometric values: $\sin 45^{\circ} = \frac{1}{\sqrt{2}}$ and $\operatorname{cosec} 30^{\circ} = 2$.So,$x 	imes \frac{1}{\sqrt{2}} = y 	imes 2$.Rearranging to find the ratio $\frac{x}{y}$: $\frac{x}{y} = 2 \sqrt{2}$.Now,calculate $\frac{x^{4}}{y^{4}}$: $\left(\frac{x}{y}ight)^{4} = (2 \sqrt{2})^{4}$.$(2 \sqrt{2})^{4} = 2^{4} 	imes (\sqrt{2})^{4} = 16 	imes 4 = 64$.Since $64 = 4^{3}$,the value is $4^{3}$.

If $x \sin 45^{\circ} = y \operatorname{cosec} 30^{\circ}$,then $\frac{x^{4}}{y^{4}}$ is equal to (in $^{3}$)

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