An alternative representation of the Vi\`ete's formula for pi by   Chebyshev polynomials of the first kind
  There are several reformulations of the Vi\`ete's formula for pi that have been reported in the modern literature. In this paper we show another analog to the Vi\`ete's formula for pi by Chebyshev polynomials of the first kind. 
S. M. Abrarov and B. M. Quine
math.NT