Mark the tick against the correct answer in the following:

Question:

Mark the tick against the correct answer in the following:

If $\cot ^{-1}\left(\frac{-1}{5}\right)=x$ then $\sin x=?$

A. $\frac{1}{\sqrt{26}}$

B. $\frac{5}{\sqrt{26}}$

C. $\frac{1}{\sqrt{24}}$

D. none of these

Solution:

Given: $\cot ^{-1} \frac{-1}{5}=x$

To Find: The value of $\sin x$

Since, $x=\cot ^{-1} \frac{-1}{5}$

$\Rightarrow \cot x=\frac{-1}{5}=\frac{\text { adjacent side }}{\text { opposite side }}$

By pythagorus theroem,

(Hypotenuse $)^{2}=(\text { opposite side })^{2}+(\text { adjacent side })^{2}$

Therefore, Hypotenuse $=\sqrt{26}$

$\Rightarrow \sin \mathrm{x}=\frac{\text { opposite side }}{\text { hypotenuse }}=\frac{5}{\sqrt{2} 6}$

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