The expression cos(2x) is a trigonometric identity and can be expressed in multiple forms depending on the context. Here are the common forms:
1. Double Angle Identity
$$ \cos(2x) = 2\cos^2(x) - 1 $$
2. Double Angle Identity (Alternative Form)
$$ \cos(2x) = 1 - 2\sin^2(x) $$
3. Using the Cosine of Sum Formula
$$ \cos(2x) = \cos(x + x) = \cos^2(x) - \sin^2(x) $$
4. Using the Sine and Cosine of Double Angle
$$ \cos(2x) = \cos^2(x) - \sin^2(x) $$
5. Using the Tangent Identity
$$ \cos(2x) = \frac{1 - \tan^2(x)}{1 + \tan^2(x)} $$
6. Using the Secant Identity
$$ \cos(2x) = \frac{1}{\sec^2(2x)} $$
7. Using the Cosine of a Sum
$$ \cos(2x) = \cos(x + x) = \cos(x)\cos(x) - \sin(x)\sin(x) = \cos^2(x) - \sin^2(x) $$
8. Using the Sine of a Double Angle
$$ \cos(2x) = \cos^2(x) - \sin^2(x) $$
Let me know if you want a specific form or if you're working with a particular problem (e.g., solving an equation, simplifying, etc.)!