(cos²A)³-(sin²A)³= cos2A(1-1/4sin²2A)
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Step-by-step explanation:
(cos²A)³-(sin²A)³
(cos²A-sin²A){(cos²A)²+(sin²A)²+sin²Acos²A}
cos2A(cos⁴A+sin⁴A+sin²Acos²A)
cos2A{(cos²A)²+(sin²A)²+sin²Acos²A}
cos2A{(cos²A+sin²A)²-2sin²Acos²A+sin²Acos²A}
cos2A(1²-sin²Acos²A)
cos2A{1-(4sin²Acos²A)/4}
cos2A{1-(2sinAcosA)²/4}
cos2A(1-sin²2A/4)
cos2A(1-1/4sin²2A)
#666
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