Choose the INCORRECT statement(s). | vedclass

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(D) For option $A$: Let $x = \sin^2 	heta$. The equation is $x^2 - x - 1 = 0$. The roots are $x = \frac{1 \pm \sqrt{5}}{2}$. Since $\sin^2 	heta$ mu

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All of the above

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(D) For option $A$: Let $x = \sin^2 	heta$. The equation is $x^2 - x - 1 = 0$. The roots are $x = \frac{1 \pm \sqrt{5}}{2}$. Since $\sin^2 	heta$ must be in $[0, 1]$,we check $\frac{1 + \sqrt{5}}{2} \approx 1.618 > 1$ and $\frac{1 - \sqrt{5}}{2} For option $B$: $	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}{16 - 3}} = \frac{\sqrt{3}(4 + \sqrt{3} - 4 + \sqrt{3})}{13 + 3} \cdot \frac{13}{13} = \frac{6}{16} = \frac{3}{8}$. Since $3/8$ is rational,the statement that it must be irrational is $INCORRECT$.For option $C$: $\sin(2)$ (radians) is in the $2^{nd}$ quadrant (positive),$\sin(3)$ is in the $2^{nd}$ quadrant (positive),and $\sin(5)$ is in the $4^{th}$ quadrant (negative). The product $(+) \cdot (+) \cdot (-) = (-)$. Thus,the statement is $INCORRECT$.Since $A, B,$ and $C$ are all incorrect,$D$ is the correct choice.

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

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