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(D) Analysis of statements:$[A]$ Let $x = \sin^2 	heta$. The equation becomes $x^2 - x - 1 = 0$. The roots are $x = \frac{1 \pm \sqrt{1 - 4(1)(-1)}}{

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All of the above

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(D) Analysis of statements:$[A]$ Let $x = \sin^2 	heta$. The equation becomes $x^2 - x - 1 = 0$. The roots are $x = \frac{1 \pm \sqrt{1 - 4(1)(-1)}}{2} = \frac{1 \pm \sqrt{5}}{2}$. Since $x = \sin^2 	heta$ must be in $[0, 1]$,and $\frac{1 + \sqrt{5}}{2} \approx 1.618 > 1$ and $\frac{1 - \sqrt{5}}{2} $[B]$ $	an(A - B) = \frac{	an A - 	an B}{1 + 	an A 	an B} = \frac{\frac{\sqrt{3}}{4 - \sqrt{3}} - \frac{\sqrt{3}}{4 + \sqrt{3}}}{1 + \frac{3}{(4 - \sqrt{3})(4 + \sqrt{3})}} = \frac{\sqrt{3}(4 + \sqrt{3} - 4 + \sqrt{3})}{16 - 3 + 3} = \frac{\sqrt{3}(2\sqrt{3})}{16} = \frac{6}{16} = \frac{3}{8}$. Since $3/8$ is rational,the statement that it must be irrational is incorrect.$[C]$ In radians: $2$ rad is in the $2^{nd}$ quadrant $(\sin 2 > 0)$,$3$ rad is in the $2^{nd}$ quadrant $(\sin 3 > 0)$,and $5$ rad is in the $4^{th}$ quadrant $(\sin 5 Since $A, B,$ and $C$ are all incorrect,the correct choice is $D$.

Choose the $INCORRECT$ statement$(s)$.

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