convert 'cos(arcsin2x)' into an algebraic form

[icyhot2590]

converting into an algebraic form

cos(arcsin2x)

is it cos(2/sqrt (1-(2x))2

 

[galactus]

No, it's \(\displaystyle \L\\\sqrt{1-4x^{2}}\)....why?.

 

[pka]

\(\displaystyle \L \begin{array}{rcl}
y & = & \arcsin (2x) \\
\sin (y) & = & 2x \\
\cos (y) & = & \sqrt {1 - 4x^2 } \\
\cos (\arcsin (2x)) & = & \sqrt {1 - 4x^2 } \\
\end{array}\)