Cosine Double Angle

This identity rewrites the cosine of twice an angle in terms of the sine and cosine of the original angle. It comes from expanding the angle-addition formula, since \(\cos(\theta+\theta)=\cos\theta\cos\theta-\sin\theta\sin\theta\). A useful equivalent form is \(\cos(2\theta)=1-2\sin^2\theta=2\cos^2\theta-1\), which lets you compute double angles from a single trig value.

Use this when you need to simplify trig expressions, solve equations involving double angles, or rewrite everything in terms of just sine or just cosine. It is also common in algebra, calculus, and physics problems involving periodic motion or rotations.

• Using \(\cos(2\theta)=2\cos\theta\) or doubling the cosine value instead of the angle
• Forgetting to square both \(\sin\theta\) and \(\cos\theta\) in the identity
• Mixing up the sign and writing \(\cos(2\theta)=\cos^2\theta+\sin^2\theta\), which is actually equal to 1