sin x - cos x = 2/3, berapa sin x + cos x

Mapel : Matematika
Kelas : X SMA
Materi : Trigonometri

Pembahasan :
Sin x - Cos x = 2/3
(Sin x - Cos x)² = (2/3)²
Sin²x + Cos²x - 2Sin x Cos x = 4/9
1 - 2Sin x Cos x = 4/9
2Sin x Cos x = 1 - 4/9
2Sin x Cos x = 5/9

(Sin x + Cos x)² = Sin²x + Cos²x + 2Sin x Cos x
(Sin x + Cos x)² = 1 + 5/9
(Sin x + Cos x)² = 14/9
Sin x + Cos x = √[14/9]
Sin x + Cos x = 1/3 √14