Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 4 / 5F / b

Table of contents
- Solution b

Solution

The recurrence shows that

T_{n}

is a polynomial with integer coefficients. Part (a) gives

T_{n} (cos (π / n)) + 1 = cos π + 1 = 0.

Thus $cos (π / n)$ is a root of a nonzero integer polynomial and is algebraic.

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