Answer
$d$
Work Step by Step
$\dfrac{2\tan{x}}{1+\tan^2{x}} = \dfrac{2\tan{x}}{\sec^2{x}}= 2 \tan{x}\cos^2{x}$
$= 2 \,\dfrac{\sin{x}}{\cos{x}} \, \cos^2{x} = 2 \sin{x} \cos{x} = \sin{2x}$
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