Solve this


If $\tan x=\frac{-5}{12}$ and $\frac{\pi}{2}



Given: $\tan x=-\frac{5}{12}$

To find: sin 2x

We know that,

$\sin 2 x=\frac{2 \tan x}{1+\tan ^{2} x}$

Putting the values, we get

$\sin 2 x=\frac{2 \times\left(-\frac{5}{12}\right)}{1+\left(-\frac{5}{12}\right)^{2}}$

$\sin 2 x=\frac{-\frac{5}{6}}{1+\frac{25}{144}}$

$\sin 2 x=\frac{-5}{6\left(\frac{144+25}{144}\right)}$

$\sin 2 x=\frac{-5 \times 144}{6 \times 169}$

$\sin 2 x=\frac{-5 \times 24}{169}$

$\sin 2 x=-\frac{120}{169}$


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