From d1d5c1f91d55a23b97880240be47e4467d5eb609 Mon Sep 17 00:00:00 2001
From: Davit Potoyan <david.potoyan@gmail.com>
Date: Mon, 26 Aug 2024 10:27:55 -0500
Subject: [PATCH] 'math symplified'

---
 math/note01.md | 11 ++++-------
 1 file changed, 4 insertions(+), 7 deletions(-)

diff --git a/math/note01.md b/math/note01.md
index 946c72a0..822f88db 100644
--- a/math/note01.md
+++ b/math/note01.md
@@ -68,12 +68,9 @@
 
 |Description|Equations|
 |-:|:-|
-|Integral of odd power of cosine <br/> $(u = \sin x)$|$\int \sin^m(x)\cos^{2k+1}(x) \ dx \newline = \int \sin^m(x) [\cos^2 (x)]^k \ dx \newline = \int \sin^m(x)[1-\sin^2(x)]^k \ dx$|
-|Integral of odd power of sine <br/> $(u = \cos x)$|$\int \sin^{2k+1}(x)\cos^{n}(x) \ dx \newline = \int [\sin^2 (x)]^k \cos^n(x) \sin(x) \ dx \newline = \int [1-\cos^2(x)]^k \cos^n(x) \sin(x) \ dx$|
-|Integral of even power of sine and cosine use trig identities|$\sin^2(x) = \frac{1}{2}(1-\cos(2x)) \newline \cos^2(x) = \frac{1}{2}(1+\cos(2x)) \newline \sin(x)\cos(x) = \frac{1}{2}\sin(2x)$|
-|Trig identity for solving <br/> $\int \sin(mx)\cos(nx) \ dx$|$\sin A \cos B = \frac{1}{2}[\sin(A-B) + \sin(A+B)]$|
-|Trig identity for solving <br/> $\int \sin(mx)\sin(nx) \ dx$|$\sin A \sin B = \frac{1}{2}[\cos(A-B) - \cos(A+B)]$|
-|Trig identity for solving <br/> $\int \cos(mx)\cos(nx) \ dx$|$\cos A \cos B = \frac{1}{2}[\cos(A-B) + \cos(A+B)]$|
-
+| Integral of even power of sine and cosine using trig identities | $\sin^2(x) = \frac{1}{2}(1-\cos(2x)) \newline \cos^2(x) = \frac{1}{2}(1+\cos(2x)) \newline \sin(x)\cos(x) = \frac{1}{2}\sin(2x)$ |
+| Trig identity for solving <br/> $\int \sin(mx)\cos(nx) \, dx$ | $\sin A \cos B = \frac{1}{2}[\sin(A-B) + \sin(A+B)]$ |
+| Trig identity for solving <br/> $\int \sin(mx)\sin(nx) \, dx$ | $\sin A \sin B = \frac{1}{2}[\cos(A-B) - \cos(A+B)]$ |
+| Trig identity for solving <br/> $\int \cos(mx)\cos(nx) \, dx$ | $\cos A \cos B = \frac{1}{2}[\cos(A-B) + \cos(A+B)]$ |