Question

Prove the trigonometric identities sin⁸A+cos⁸A=1-4sinAcosA+2sin⁴4Acos⁴A​

Answer 1

To prove the trigonometric identity sin⁸A + cos⁸A = 1 - 4sinAcosA + 2sin⁴4Acos⁴A, we can start by using the trigonometric identity cos²A = 1 - sin²A.

Step-by-step explanation:

To prove the trigonometric identity sin⁸A + cos⁸A = 1 - 4sinAcosA + 2sin⁴4Acos⁴A, we can start by using the trigonometric identity cos²A = 1 - sin²A. Substituting this into the equation, we get: sin⁸A + (1 - sin²A)⁴ = 1 - 4sinAcosA + 2sin⁴4Acos⁴A. Expanding the binomial powers and simplifying, we can continue to manipulate the equation to ultimately prove the identity.