complete the identity:
sin^4x-cos^4x
To complete the identity sin^4(x) - cos^4(x), we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).
Using the difference of squares formula, we rewrite sin^4(x) - cos^4(x) as (sin^2(x) + cos^2(x))(sin^2(x) - cos^2(x)).
Now, we know that sin^2(x) + cos^2(x) is equal to 1, as it is one of the fundamental trigonometric identities.
Therefore, the identity sin^4(x) - cos^4(x) can be simplified to 1 * (sin^2(x) - cos^2(x)), which gives us sin^2(x) - cos^2(x).
So, the complete identity is sin^4(x) - cos^4(x) = sin^2(x) - cos^2(x).