From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Fri, 15 Mar 2019 01:43:23 +0000 (+1100)
Subject: [spec] corrections in double angle formulas
X-Git-Tag: yr12~205
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/93c11efe55ab01fff6d54386d5e8152bcd749964

[spec] corrections in double angle formulas
---

diff --git a/spec/circ.md b/spec/circ.md
index c3c5b17..a5dae02 100644
--- a/spec/circ.md
+++ b/spec/circ.md
@@ -77,7 +77,9 @@ $$\tan(x \pm y) = {{\tan x \pm \tan y} \over {1 \mp \tan x \tan y}}$$
 ## Double angle formulas
 
 \begin{equation}\begin{split}
-  \cos 2x = \cos^2 x = \sin^2 x
+  \cos 2x &= \cos^2 x - \sin^2 x \\
+  & = 1 - 2\sin^2 x \\
+  & = 2 \cos^2 x -1
 \end{split}\end{equation}
 
 $$\sin 2x = 2 \sin x \cos x$$
diff --git a/spec/circ.pdf b/spec/circ.pdf
index 4f0cd66..bb10a7f 100644
Binary files a/spec/circ.pdf and b/spec/circ.pdf differ