 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-1/section-a/7/solution

The double-angle identity for the sine factors the equation as

2 cos θ (sin θ - cos θ) = 0

. The first factor gives

θ = π /2

in the specified interval; the second gives

tan θ = 1

and hence

θ = π /4

. Thus

θ = \frac{π}{4}, \frac{π}{2} .

Keeping the first factor avoids losing the solution where division by

cos θ

would be invalid.

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