From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Thu, 14 Mar 2019 01:09:53 +0000 (+1100)
Subject: [spec] compound & double angle formulas
X-Git-Tag: yr12~208
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/12b67db7ce87e6b95dad19f4399d21e20ef50069?ds=sidebyside

[spec] compound & double angle formulas
---

diff --git a/spec/circ.md b/spec/circ.md
index 9d7dfbf..c3c5b17 100644
--- a/spec/circ.md
+++ b/spec/circ.md
@@ -67,3 +67,20 @@ $$\operatorname{cot} \theta = {{\cos \theta} \over {\sin \theta}} \> \vert \> \s
   1 + \operatorname{cot}^2 x & = \operatorname{cosec}^2 x, \quad \text{where } \sin x \ne 0 \\
   1 + \tan^2 x & = \operatorname{sec}^2 x, \quad \text{where } \cos x \ne 0
 \end{split}\end{equation}
+
+## Compound angle formulas
+
+$$\cos(x \pm y) = \cos x + \cos y \mp \sin x \sin y$$
+$$\sin(x \pm y) = \sin x \cos y \pm \cos x \sin y$$
+$$\tan(x \pm y) = {{\tan x \pm \tan y} \over {1 \mp \tan x \tan y}}$$
+
+## Double angle formulas
+
+\begin{equation}\begin{split}
+  \cos 2x = \cos^2 x = \sin^2 x
+\end{split}\end{equation}
+
+$$\sin 2x = 2 \sin x \cos x$$
+
+$$\tan 2x = {{2 \tan x} \over {1 - \tan^2 x}}$$
+