Question:
If $\cos \mathrm{x}=\frac{-3}{5}$ and $\pi<\mathrm{x}<\frac{3 \pi}{2}$ find the values of cos 2x
Solution:
Given: $\cos \mathrm{x}=\frac{-3}{5}$
To find: $\cos 2 x$
We know that
$\cos 2 x=2 \cos ^{2} x-1$
Putting the value, we get
$\cos 2 x=2\left(-\frac{3}{5}\right)^{2}-1$
$\cos 2 x=2 \times \frac{9}{25}-1$
$\cos 2 x=\frac{18}{25}-1$
$\cos 2 x=\frac{18-25}{25}$
$\therefore \cos 2 \mathrm{x}=-\frac{7}{25}$