Prove thtat cos^4 A - sin^4 A + 1 = 2cos^2 A?

Question

please explain to me how you would prove the above equation

Answer 1

cos⁴A - sin⁴A + 1

  (a⁴ - b⁴) = (a² -b²)(a² + b²)

= [(cos²A - sin²A)( cos²A + sin²A)] + 1

 Recall : cos²A + Sin²A = 1

= (cos²A - sin²A)(1) + 1

(cos²A - sin²A) + 1

Recall : cos²A - (1 - cos²A) + 1

cos²A  - 1 + cos²A + 1

2cos²A.