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

1 Answer

Dec 6, 2015

#sqrt(1-x^2)#.

Explanation:

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

#sqrt(1-sin^2(arcsin(x))#

And since #sin(arcsin(x))=x#, then #sin^2(arcsin(x))=x^2#.

So, your expression becomes #sqrt(1-x^2)#.

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