Question:
If $\tan \mathrm{x}=\frac{-5}{12}$ and $\frac{\pi}{2}<\mathrm{x}<\pi$ find the values of cos 2x
Solution:
Given: $\tan \mathrm{x}=-\frac{5}{12}$
To find: cos 2x
We know that,
$\cos 2 x=\frac{1-\tan ^{2} x}{1+\tan ^{2} x}$
Putting the values, we get
$\cos 2 x=\frac{1-\left(-\frac{5}{12}\right)^{2}}{1+\left(-\frac{5}{12}\right)^{2}}$
$\cos 2 x=\frac{1-\frac{25}{144}}{1+\frac{25}{144}}$
$\cos 2 x=\frac{\frac{144-25}{144}}{\left(\frac{144+25}{144}\right)}$
$\cos 2 x=\frac{\frac{119}{144}}{\frac{169}{144}}$
$\cos 2 x=\frac{119}{169}$
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