 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-1/8/a/solution

cos x = 2 sin x cos x

, or

cos x (1 - 2 sin x) = 0

. Preserve both factors:

cos x = 0

contributes the endpoint, while

sin x = 1/2

contributes the interior solution. In the specified interval,

x = \frac{π}{6}, \frac{π}{2} .

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