jika sin x - cos x =1/4 . tentukan nilai dari 8 sin x. cosx

Bab Trigonometri
Matematika SMA Kelas X

sin x - cos x = 1/4
(sin x - cos x) = (1/4)²
sin² x - 2 sin x cos x + cos² x =1/16
(sin² x + cos² x) - 2 sin x cos x = 1/16
1 - 2 sin x cos x = 1/16
2 sin x cos x = 1 - 1/16
2 sin x cos x = 15/16

8 sin x cos x = 4 . (2 sin x cos x)
8 sin x cos x = 4 . 15/16
8 sin x cos x = 15/4