$\sqrt[]{d_1}and\sqrt[]{d_2}$ are the impact parameters corresponding to scattering angles 60° and 90° respectively, when an a particle is approaching a gold nucleus. For d₁ = x d₂, the value of x will be________.

<p><span contenteditable="false"> <math> <mrow> <mroot> <mrow> <mi>d</mi> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span><span contenteditable="false"> <math> <mrow> <mi>c</mi> <mi>o</mi> <mi>t</mi> <mfrac> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> </span></p><p>cot² 30° = x cot² 45°</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; x = 3</p>

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