# Real Analysis Problem

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The inverse cosine function has domain [-1,1]and range [0, pi]. Prove that (cos^-1)'(x) = -1/ sqrt(1-x^2).

This needs to be proved from a real analysis point of view not a calculus.

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#### Solution Preview

Let y = cos^-1(x)

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<br>So now we need to prove that dy/dx = -1/sqrt(1-x^2)

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<br>Let x = cos(t)------eqn 1

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<br>Therefor y = cos^-1(cos(t))

<br> or y = t (because cos^-1 of cos means just ...

#### Solution Summary

The inverse cosine functions of domain are analyzed. The expert proves from a real analysis point of view not a calculus.

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