Question

(cos⁴A - sin⁴A) is equal to


1. 1 - 2cos²A
2. 2sin²A - 1
3. sin²A - cos²A
4. 2cos²A - 1​

Answer 1

.

Well, cos⁴A - sin⁴A = (cos²A + sin²A)(cos²A - sin²A)

Now, cos²A + sin²A ≡ 1

=> cos²A - sin²A ≡ cos2A

Well, cos(A + B) ≡ cosAcosB - sinAsinB

Replacing B with A we get:

cos(A + A) ≡ cosAcosA - sinAsinA => cos²A - sin²A

Hence, cos2A ≡ cos²A - sin²A

hope the answer is correct