Sin^8A+cos^8A=1-4sin^A*cos^2A+2sin^4A*cos^4A
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Answer:
Step-by-step explanation:
sin²A + cos²A = 1
//squaring on both sides
(sin²A + cos²A)² = 1²
=> sin⁴A + cos⁴A + 2sin²Acos²A = 1
=> sin⁴A + cos⁴A = 1 - 2sin²Acos²A
//squaring on both sides again
(sin⁴A + cos⁴A)² = (1 - 2sin²Acos²A)²
=> sin⁸A + cos⁸A + 2sin⁴Acos⁴A = 1 + 4sin⁴Acos⁴A - 4sin²Acos²A
=> sin⁸A + cos⁸A = 1 + 2sin⁴Acos⁴A - 4sin²Acos²A
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