 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-1/5/solution

cos 2 x = 1 - 2 sin^{2} x

. Setting

s = sin x

reduces the equation to

2 s^{2} + s - 1 = (2 s - 1) (s + 1) = 0

. On

0 \leq x \leq π

, the sine is nonnegative, so only

s = 1/2

is allowed. Therefore

x = \frac{π}{6} or x = \frac{5 π}{6} .

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