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