Question

Q1 (cos⁴A − sin⁴A) is equal to
(a) 1 − 2 cos²A
(b) 2 sin²A − 1
(c) sin²A − cos²A
(d) 2 cos²A − 1

Answer 1

Answer:

2cos²A - 1

Step-by-step explanation:

=> cos⁴A - sin⁴A

=> (cos²A)² - (sin²A)²

Using a² - b² = (a + b)(a - b)

=> (cos²A + sin²A)(cos²A - sin²A)

Using sin²x + cos²x = 1

=> 1(cos²A - sin²A)

=> cos²A - sin²A

=> cos²A - (1 - cos²A)

=> cos²A - 1 + cos²A

=> 2cos²A - 1