Find the value of [2 ^ -1 (-5 12 ) ] - Vidyadip

Question

Find the value of $\sin \left[2 \cot ^{-1}\left(\frac{-5}{12}\right)\right]$

✓

Answer

Let $\cot ^{-1}\left(\frac{-5}{12}\right)=y$
Then $\cot y=\frac{-5}{12}$
Now,
$\sin \left[2 \cot ^{-1}\left(\frac{-5}{12}\right)\right]=\sin 2 y$
$=2 \sin y \cos y=2\left(\frac{12}{13}\right)\left(\frac{-5}{13}\right) $
$\left[\text { since } \cot y<0, \text { so } y \in\left(\frac{\pi}{2}, \pi\right)\right]$
$=\frac{-120}{169}$

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