Problem 9 - Entrance Test

If sin(2x) = 2sin x cos x and tan y = 1/√3, find the value of x and y.

A. x = 30°, y = 30°B. x = 30°, y = 45°C. x = 45°, y = 30°D. x = 30°, y = 60°

Correct: A

Given sin(2x) = 2sin x cos x. Using the trigonometric identity sin(2x) = 2sin x cos x, we can write 2sin x cos x = 2sin x cos x. This is always true for any value of x, so x can be any angle. Given tan y = 1/√3. As tan(30°) = 1/√3, y = 30°. Thus the value of x is any angle and y = 30°.