2.1 / U.e 2.8 to cxpand \( \cos 2 \alpha \)
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To expand \( \cos 2\alpha \), we can use the double angle formula which states that \( \cos 2\alpha = \cos^2 \alpha - \sin^2 \alpha \). This can also be rewritten using the Pythagorean identity \( \sin^2 \alpha + \cos^2 \alpha = 1 \), resulting in another version: \( \cos 2\alpha = 2\cos^2 \alpha - 1 \) or \( \cos 2\alpha = 1 - 2\sin^2 \alpha \). Choose the version that best suits your needs for further calculations! Additionally, if you’re working on trigonometric identities, it’s super helpful to visualize these with the unit circle. Picture the angle \( \alpha \) and its corresponding sine and cosine values. This mental image can simplify many problems, allowing you to see how the cosine value behaves with changes in angles, especially as you explore transformations like rotations!
