Solve this


If $\cos \mathrm{X}=\frac{-3}{5}$ and $\pi<\mathrm{x}<\frac{3 \pi}{2}$ find the values of tan 2x



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

$\tan 2 x=\frac{\frac{24}{25}}{-\frac{7}{25}}$

$\tan 2 x=\frac{24}{25} \times\left(-\frac{25}{7}\right)$

$\therefore \tan 2 \mathrm{x}=-\frac{24}{7}$


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