 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/10/solution

Use

2 cos^{2} x = 1 + cos 2 x

to reduce the equation to

sin 2 x = cos 2 x

. Equivalently,

2 sin (2 x - π /4) = 0

, so

x = π /8 + kπ /2

k

. Restricting to

[0, π]

gives

x = \frac{π}{8}, x = \frac{5 π}{8} .

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