Answer
$cos~(arcsin~u) = \sqrt{1-u^2}$
Work Step by Step
Let $~~\theta = arcsin~u$
Then $~~sin~\theta = u$
$cos~\theta = \sqrt{1-sin^2~\theta}$
$cos~\theta = \sqrt{1-u^2}$
Therefore, $~~cos~(arcsin~u) = \sqrt{1-u^2}$
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