If cot - 1 ( - 1 5 ) = , the value of sin is:

Question

If $\cot^{- 1} (- \frac{1}{5}) = θ$ , the value of $\sin θ$ is:

Smart Achievers · Accepted Answer

(4)

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

Explanation:

Given, $\cot^{- 1} (\frac{- 1}{5}) = θ, where θ \in (0, π)$

$∴$ $\cot θ = \frac{- 1}{5}$

$∵$ $\sin θ = \frac{1}{c o s e c θ} = \frac{1}{\sqrt{1 + \cot^{2} θ}}$

$= \frac{1}{\sqrt{1 + {(- \frac{1}{5})}^{2}}} = \frac{1}{\sqrt{1 + \frac{1}{25}}} = \frac{1}{\sqrt{\frac{26}{25}}}$

$= \frac{5}{\sqrt{26}}$

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