Question:
If $\cos \mathrm{X}=\frac{-3}{5}$ and $\pi<\mathrm{x}<\frac{3 \pi}{2}$ find the values of tan 2x
Solution:
To find: tan2x
From part (i) and (ii), we have
$\sin 2 x=\frac{24}{25}$
and $\cos 2 \mathrm{x}=-\frac{7}{25}$
We know that,
$\tan x=\frac{\sin x}{\cos x}$
Replacing x by 2x, we get
$\tan 2 x=\frac{\sin 2 x}{\cos 2 x}$
Putting the values of sin 2x and cos 2x, we get
$\tan 2 x=\frac{\frac{24}{25}}{-\frac{7}{25}}$
$\tan 2 x=\frac{24}{25} \times\left(-\frac{25}{7}\right)$
$\therefore \tan 2 \mathrm{x}=-\frac{24}{7}$