 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-4/5f/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The recurrence and the addition formula give the result by induction. It is true for

n = 0, 1

, and if true for

n, n - 1

, then

T_{n + 1} (cos y) = 2 cos y cos (n y) - cos ((n - 1) y) = cos ((n + 1) y) .

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