C-09-Q112mediumsingle_mcqIf xy=7−43\dfrac{x}{y} = 7 - 4\sqrt{3}yx=7−43, where x=cosecA−cotAx = \operatorname{cosec} A - \cot Ax=cosecA−cotA, y=cosecA+cotAy = \operatorname{cosec} A + \cot Ay=cosecA+cotA, then A=?A = ?A=?a30∘30^\circ30∘b45∘45^\circ45∘c60∘60^\circ60∘d75∘75^\circ75∘ব্যাখ্যাSince xy=1xy=1xy=1, xy=x2=7−43=(2−3)2\dfrac{x}{y}=x^2=7-4\sqrt3=(2-\sqrt3)^2yx=x2=7−43=(2−3)2, so x=cosecA−cotA=2−3x=\operatorname{cosec} A-\cot A=2-\sqrt3x=cosecA−cotA=2−3. This value occurs at A=30∘A=30^\circA=30∘, where cosec30∘−cot30∘=2−3\operatorname{cosec}30^\circ-\cot30^\circ=2-\sqrt3cosec30∘−cot30∘=2−3.