Double-angle formulae
sin 2x = 2 sin x cos x; cos 2x = cos²x − sin²x; tan 2x = 2 tan x / (1 − tan²x).
Three forms for cos 2x: cos²x − sin²x = 1 − 2 sin²x = 2 cos²x − 1. Pick whichever fits the equation. Half-angle formulae follow.
Worked examples
If sin x = 3/5, cos x = 4/5, then sin 2x = 24/25.
cos 2x = 1 − 2 sin²x lets you express in terms of sin x only.
Integrating sin²x: use cos 2x = 1 − 2 sin²x to convert.
Frequently asked questions
Half-angle?
x = 2(x/2). cos x = 1 − 2 sin²(x/2) etc.
Why three cos 2x forms?
Each useful in a different context (e.g. integration, equations).