cos(2θ) =

To find the expression for $\cos(2\theta)$, we use the **cosine addition formula**: $$\cos(A + B) = \cos A \cos B - \sin A \sin B$$ ### Step 1: Substitution Since we want to find $\cos(2\theta)$, we can rewrite $2\theta$ as $(\theta + \theta)$. By letting $A = \theta$ and $B = \theta$, we substitute these into the addition formula: $$\cos(\theta + \theta) = \cos \theta \cos \theta - \sin \theta \sin \theta$$ ### Step 2: Simplify the expression Now, we multiply the terms: - $\cos \theta \cdot \cos \theta = \cos^2\theta$ - $\sin \theta \cdot \sin \theta = \sin^2\theta$ Putting it together, we get: $$\cos(2\theta) = \cos^2\theta - \sin^2\theta$$ This is one of the standard double-angle identities for cosine.