What is the identity for cos(2x)?

The identity for cos(2x) can be represented in multiple forms, which is why it is accurate to say that all the provided options are indeed valid representations of this identity.

The fundamental trigonometric identity for cos(2x) can be expressed as:

1. The first form, cos(2x) = cos²(x) - sin²(x), directly arises from the double angle formula for cosine. This form shows the relationship between cosine and sine for double angles.

2. The second form can be derived from the first identity using the Pythagorean identity, sin²(x) = 1 - cos²(x), which leads to cos(2x) = cos²(x) - (1 - cos²(x)) = 2cos²(x) - 1.

3. The third form can also be derived similarly, starting from sin²(x) expressed in terms of cos²(x). By using sin²(x) = 1 - cos²(x), we can re-arrange to yield cos(2x) as 1 - 2sin²(x).

Since each form can be derived from the others using basic trigonometric identities, they all represent the same value for cos(2x