 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-1/5/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

The double-angle identity

cos (2 x) = 2 cos^{2} x - 1

reduces the equation to

cos x (1 + 2 cos x) = 0

. On the specified interval the cosine takes each of the values

0

and

- 1/2

once, giving

x = \frac{π}{2}, x = \frac{2 π}{3} .

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