jika sin α + cos α = 6/5 ,hitunglah : a. sin α . cos α b. sin ^3 α + cos ^3 α

Bab Trigonometri
Matematika SMA Kelas X

sin a + cos a = 6/5

a] (sin a + cos a)² = (6/5)²
sin² a + 2 sin a cos a + cos² a = 36/25
sin² a + cos² a + 2 sin a cos a = 36/25
1 + 2 sin a cos a = 36/25
2 sin a cos a = 36/25 - 1
2 sin a cos a = 36/25 - 25/25
sin a . cos a = 11/(2 . 25)
sin a . cos a = 11/50

b] sin^3 a + cos^3 a
= (1/2) . (sin a + cos a) . (2 - 2 sin a cos a)
= (1/2) . (6/5) . (2 - 2 . 11/50)
= (3/5) . (2 . 50 - 22)/50
= (3/5) . (78/50)
= 234/250
= 117/125

Trigonometri

sin α + cos α =  6/5

a) sin α cos a  = 1/2  { (sin α +cos α)² -1}
sin α cos α = 1/2 ({ (6/5)² - 1} = 1/2 (36/25 - 1) = 1/2 (11/25)
sin α cos α = 11/50

b) sin³ α + cos³ α = (sin α + cos α)³ - 3(sin α cos α)(sin α+ cos α)
sin³ α + cos³ α =  (6/5)³ - 3(11/50)(6/5) = 216/125 - 99/125
sin³ α + cos³ α = 117/125
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