Question

prove that:

cos8A+sin8A = 1-2sin²2A+1/8sin⁴2A​

Answer 1

Answer:

prove

Step-by-step explanation:

cos⁸A+sin⁸A = (Cos⁴A)² + (Sin⁴A)²

=> (Cos⁴A + Sin⁴A)² - 2Cos⁴ASin⁴A

=> [(Cos²A)²+(Sin²A)²]² - 2(CosASinA)⁴

=> [(Cos²A+Sin²A)² - 2Cos²ASin²A]² - 2(CosASinA)⁴

=> [1 - 2Cos²ASin²A]² - 2(CosASinA)⁴

=> [1 - 2(CosASinA)²]² - 2(CosASinA)⁴

//Remember: Sin2A = 2SinA CosA => SinACosA = 1/2Sin2A

=> [1 - 2(1/2Sin2A)²]²- 2(1/2Sin2A)⁴

=> [1 - 1/2Sin²2A]² - 1/8Sin⁴2A

=> 1 + 1/4Sin⁴2A - Sin²2A - 1/8Sin⁴2A

=> 1 - Sin²2A + 1/8Sin⁴2A

=> R.H.S