How do you find an equivalent algebraic expression for the composition cos(arcsin(x))?

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How do you find an equivalent algebraic expression for the composition cos(arcsin(x))?

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Answer 1 · 2015-12-06T13:58:52

$\sqrt{1 - x^{2}}$ $sqrt(1-x^2)$ .

Explanation:

Since ${cos}^{2} (x) = 1 - {sin}^{2} (x)$ $cos^2(x)=1-sin^2(x)$ , you have that $cos (x) = \pm \sqrt{1 - {sin}^{2} (x)}$ $cos(x)=\pm\sqrt(1-sin^2(x))$ . So, your expression becomes

$\sqrt{1 - {sin}^{2} (arcsin (x))}$ $sqrt(1-sin^2(arcsin(x))$

And since $sin (arcsin (x)) = x$ $sin(arcsin(x))=x$ , then ${sin}^{2} (arcsin (x)) = x^{2}$ $sin^2(arcsin(x))=x^2$ .

So, your expression becomes $\sqrt{1 - x^{2}}$ $sqrt(1-x^2)$ .

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How do you find an equivalent algebraic expression for the composition cos(arcsin(x))?

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