Selesaikanlah jika sin α + cos α = 1/3 maka nilai sin³ α - cos³ α
Suhartono
Sin³ a - cos³ a = (sin a + cos a)(sin² a - sin a cos a + cos² a) = (sin a + cos a)((sin a + cos a)² - 3sin a cos a) ingat: (sin a + cos a)² = 1/9 1 + 2 sin a cos a = 1/9 sin a cos a = -4/9 maka (sin a + cos a)((sin a + cos a)² - 3sin a cos a) = 1/3 . (1/9 + 12/9) = 1/3 . 13/9 = 13/27 jawaban: 13/27
1 votes Thanks 1
andiina
13/27 hasilnya bisa di perkecil lagi? dalam bentuk akar?
= (sin a + cos a)(sin² a - sin a cos a + cos² a)
= (sin a + cos a)((sin a + cos a)² - 3sin a cos a)
ingat:
(sin a + cos a)² = 1/9
1 + 2 sin a cos a = 1/9
sin a cos a = -4/9
maka
(sin a + cos a)((sin a + cos a)² - 3sin a cos a)
= 1/3 . (1/9 + 12/9)
= 1/3 . 13/9
= 13/27
jawaban: 13/27