Solve this


If $\tan \mathrm{x}=\frac{-5}{12}$ and $\frac{\pi}{2}<\mathrm{x}<\pi$ find the values of tan 2x



Given: $\tan \mathrm{x}=-\frac{5}{12}$

To find: $\tan 2 x$

We know that,

$\tan 2 x=\frac{2 \tan x}{1-\tan ^{2} x}$

Putting the values, we get

$\tan 2 x=\frac{2 \times\left(-\frac{5}{12}\right)}{1-\left(-\frac{5}{12}\right)^{2}}$

$\tan 2 x=\frac{-\frac{5}{6}}{1-\frac{25}{144}}$

$\tan 2 x=\frac{-5}{6\left(\frac{144-25}{144}\right)}$

$\tan 2 x=\frac{-5 \times 144}{6 \times 119}$

$\tan 2 x=\frac{-5 \times 24}{119}$

$\tan 2 \mathrm{x}=-\frac{120}{119}$


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