Prove the following identity. cos4 x − sin4 x = cos 2x

    for the right-hand side, use cosine double angle identity which states that  cos 2x = cos²x - sin² x    for the left-hand side    we factor using difference of squares.recall difference of squares factoring: a² - b² = (a - b)(a + b)but here we have a⁴ - b⁴, so  a⁴  - b⁴ = (a² - b²)(a²  + b²)note that cos⁴ x is equivalent to (cos x)⁴ and etc.    note that cos²x + sin²x = 1 via the pythagorean identity