Question

Himpunan penyelesaian : cos 2x - sin x = 0, untuk 0 ≤ x ≤ 2π adalah ...............?

Answer 1

cos(2x) - sin(x) = 0
1 - 2sin²(x) - sin(x) = 0
-2 sin²(x) - sin(x) + 1 = 0
2 sin²(x) + sin(x) - 1 = 0
(2 sin(x) - 1) (sin(x) + 1) = 0
-----------------------------------------
2 sin(x) - 1 = 0
2 sin(x) = 1
sin(x) = 1/2
x = 30° atau 150°

sin(x) + 1 = 0
sin(x) = -1
x = 270°

Himpunan Penyelesaian: {30° , 150° , 270°}