Double Angle Identities

TL;DR: Double-angle formulas express trig of \(2\theta\) in terms of trig of \(\theta\): \(\sin(2\theta) = 2\sin\theta\cos\theta\), and \(\cos(2\theta)\) has three forms. Half-angle formulas find trig of \(\tfrac{\theta}{2}\). Both simplify integration and trig equations. Key takeaways: Sine double-angle: \(\sin(2\theta) = 2\sin\theta\cos\theta\). Cosine double-angle (three forms): \(\cos(2\theta) = \cos^2\theta – \sin^2\theta = 1 – 2\sin^2\theta = 2\cos^2\theta […]