Mathematics

The key is recognizing that this is a angle addition problem where you can use the cosine addition formula—but there's a shortcut. Since $\pi$ is a "special" angle where cosine equals $-1$, you can use the identity $\cos(\pi + \theta) = -\cos(\theta)$ to collapse the work into one step. This transforms an unfamiliar angle into a familiar reference angle you already know.

The key is recognizing that this is a angle addition problem where you can use the cosine addition formula—but there's a shortcut. Since $\pi$ is a "special" angle where cosine equals $-1$, you can use the identity $\cos(\pi + \theta) = -\cos(\theta)$ to collapse the work into one step. This transforms an unfamiliar angle into a familiar reference angle you already know.