diketahui sin x + cos x = p, hitunglah sin³x + cos³x !
Matematika
Muniroh17
Pertanyaan
diketahui sin x + cos x = p, hitunglah sin³x + cos³x !
1 Jawaban
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1. Jawaban Anonyme
jawab
sin x + cos x = p
(sin x + cos x)² = p²
1 + 2 sin x cos x = p²
2 sin x cos x = p² -1
sin x cos x = 1/2 (p² -1)
sin³ x + cos³ x = (sin x + cos x)³ - 3 (sin x cos x)(sin x + cos x )
= (p)³ -3(1/2)(p² -1)(p)
= p³ - 3/2 (p³ -p)
= p³ - 3/2 p³ + 3/2p
= - 1/2 p³ + 3/2 p
= - 1/2 p ( p² - 3)