A calculus problem by Satvik Choudhary

Calculus Level 4

If \[ x_{n+1}=\sqrt { \frac {1}{2} (1+x_{n})}\], then

\[\cos [\frac {\sqrt{1-x_{0} ^{2}}}{x_{1}x_{2}x_{3}...\infty}] \]

\[ |x_{0}|<1\] is equal to

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