Question

What is cos(2cos^-1x) written as an algebraic expression in x?

Answer 1

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Answer 2

\[\cos(2\theta)=2\cos^2(\theta)-1\] should do it

Answer 3

so
\[\cos(2\cos^{-1}(x))=2\cos^2(\cos^{-1}(x))-1\]

Answer 4

and since \(\cos(\cos^{-1}(x))=x\) you get your algebraic expression