If <span class="math-tex">\(\tan x = \dfrac{-3}{4}\)</span> and <span class="math-tex">\(\dfrac{3\pi}{2}< x < 2\pi\)</span>, then the value of sin 2x is
Step-by-step Solution:
\begin{aligned} \sin 2x &= \frac{2 \tan x}{1 + \tan^2 x} \\ &= \frac{2 \times \frac{-3}{4}}{1 + \left(\frac{-3}{4}\right)^2} \\ &= \frac{\frac{-3}{2}}{\frac{16 + 9}{16}} \\ &= \frac{-3}{2} \times \frac{16}{25} = \frac{-24}{25} \end{aligned}