jika sin Φ + cos Φ= 1/2 maka sin^3 Φ + cos^3 Φ
Matematika
Ftsaniyatul
Pertanyaan
jika sin Φ + cos Φ= 1/2 maka sin^3 Φ + cos^3 Φ
1 Jawaban
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1. Jawaban vivaproducation
sinx + cosx = 1/2
(sinx + cosx)² = 1/4
sin²x + cos²x + 2 sinx cosx = 1/4
1 + 2 sinx cosx = 1/4
2 sinx cosx = -3/4
sinx cosx = -3/8
sin³x + cos³x = (sinx + cosx)³ - 3 sinx cosx(sinx + cosx)
= (1/2)³ - 3(-3/8)(1/2)
= (1/8) + (9/16)
= 11/16