Math, asked by shresthapuja886, 2 months ago

Sin^8A+cos^8A=1-4sin^A*cos^2A+2sin^4A*cos^4A​

Answers

Answered by spiderman2019
0

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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