Answer
$\dfrac{24}{25}$
Work Step by Step
$\alpha =\tan^{-1} \dfrac{3}{4}$
$\tan{\alpha} = \dfrac{3}{4}$
$\sec{\alpha} =\sqrt{1+\tan^2{\alpha}} = \dfrac{5}{4}$
$\cos{\alpha} =\dfrac{1}{\sec{\alpha}} = \dfrac{4}{5}$
$\sin{\alpha} = \sqrt{1-\cos^2{\alpha}} = \dfrac{3}{5}$
$\sin{2\alpha} =2 \sin{\alpha} \cos{\alpha} =2\times \dfrac{3}{5} \times \dfrac{4}{5} = \dfrac{24}{25}$
