 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/7/solution

Since

cos x > 0

throughout the given interval, multiplying by

cos x

is reversible. The equation simplifies to

2 - sin x = 3 cos x, sin x + 3 cos x = 2 sin (x + π /3) = 2.

The sine equals

1

only at

π /2 + 2 jπ

. Here

x + π /3 \in [π /3, 5 π /6)

, so only

x + π /3 = π /2

is allowed. Hence

x = π /6.

 New to topics? Read the docs here!