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Exercise

$\sin\left(\arctan\left(\csc\left(\arccot\left(x\right)\right)\right)\right)$

Step-by-step Solution

1

Simplify $\sin\left(\arctan\left(\csc\left(\mathrm{arccot}\left(x\right)\right)\right)\right)$ as $\frac{\csc\left(\mathrm{arccot}\left(x\right)\right)}{\sqrt{\csc\left(\mathrm{arccot}\left(x\right)\right)^2+1}}$

$\frac{\csc\left(\mathrm{arccot}\left(x\right)\right)}{\sqrt{\csc\left(\mathrm{arccot}\left(x\right)\right)^2+1}}$

Final answer to the exercise

$\frac{\csc\left(\mathrm{arccot}\left(x\right)\right)}{\sqrt{\csc\left(\mathrm{arccot}\left(x\right)\right)^2+1}}$

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