Solve this


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



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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