convert 'cos(arcsin2x)' into an algebraic form

No, it's \(\displaystyle \L\\\sqrt{1-4x^{2}}\)....why?.
 
\(\displaystyle \L \begin{array}{rcl}
y & = & \arcsin (2x) \\
\sin (y) & = & 2x \\
\cos (y) & = & \sqrt {1 - 4x^2 } \\
\cos (\arcsin (2x)) & = & \sqrt {1 - 4x^2 } \\
\end{array}\)
 
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