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