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TrigonometrySuperchallengeSum, Difference, and Multiple-Angle Formulas

Sum, Difference, and Multiple-Angle Formulas · Superchallenge problem

A sequence has x1=2−3x_1 = 2 - \sqrt{3} and xn+1=2xn1−xn2x_{n+1} = \dfrac{2x_n}{1 - x_n^2} for n≥1n \ge 1. Find x2+x3x_2 + x_3.