Jika sina+cosa = 1/2, tentukan nilai sin^3 a + cos^3 a
arsetpopeye
Sin a + cos a = 1/2 (sin a + cos a)^2 = (1/2)^2 sin^2 a + 2 sin a cos a + cos^2 a = 1/4 2 sin a cos a + 1 = 1/4 2 sin a cos a = -3/4 sin a cos a = -3/8
sin^3 a + cos^3 a = (sin a + cos a)^3 - 3 sin a cos a (sin a + cos a) = (1/2)^3 - 3 (-3/8) (1/2) = 1/8 + 9/16 = 11/16
(sin a + cos a)^2 = (1/2)^2
sin^2 a + 2 sin a cos a + cos^2 a = 1/4
2 sin a cos a + 1 = 1/4
2 sin a cos a = -3/4
sin a cos a = -3/8
sin^3 a + cos^3 a
= (sin a + cos a)^3 - 3 sin a cos a (sin a + cos a)
= (1/2)^3 - 3 (-3/8) (1/2)
= 1/8 + 9/16
= 11/16