Jika ( sin teta + cos teta ) = 1/5 , tentukan nilai sin³ teta + cos³ teta

jawab

(sin t + cos t) = 1/5
(sin t + cos t)² = (1/5)²
1 + 2 sin t cos t  = 1/25
2 sin t cos t = 1/25 - 1 = -24/25
sin t  cos t = -24/50

sin³ t + cos³ t = (sin t + cos t)³ - 3 (sin t)(cos t) (sin t + cos t)
= (1/5)³ - 3(-24/50)(1/5)
= 1/125 + 72/250
= 74/250
= 37/125