(cos⁴A - sin⁴A) is equal to
1. 1 - 2cos²A
2. 2sin²A - 1
3. sin²A - cos²A
4. 2cos²A - 1
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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
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