Buktikan bahwa sin6A+cos6A=1-3sin2Acos2A
Penyelesaian:
Diberikan sin 6 A + cos 6 A
sin 6 A + cos 6 A = (sin 2 A) 3 + (cos 2 A) 3
(a + b) 3 = a 3 + b 3 + 3ab
(sin 2 A + cos 2 A) 3 = (sin 2 A+cos 2 A) 3 – 3sin 2 Acos 2 A
sin 2 A + cos 2 A = 1
(sin 2 A + cos 2 A) 3 = 1 – 3sin 2 Acos 2 A
sin 6 A + cos 6 A = 1 – 3sin 2 Acos 2 A
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