From 07cdd1c97c83a0734546796bfd24d708d0163ec6 Mon Sep 17 00:00:00 2001 From: arc Date: Wed, 3 Sep 2025 12:49:06 -0600 Subject: [PATCH] vault backup: 2025-09-03 12:49:06 --- .../MATH1220 (calc II)/Integration with Trig Identities.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1220 (calc II)/Integration with Trig Identities.md b/education/math/MATH1220 (calc II)/Integration with Trig Identities.md index 3a4261d..d89668e 100644 --- a/education/math/MATH1220 (calc II)/Integration with Trig Identities.md +++ b/education/math/MATH1220 (calc II)/Integration with Trig Identities.md @@ -2,4 +2,9 @@ The below integration makes use of the following trig identities: 1. The Pythagorean identity: $\sin^2(x) + \cos^2(x) = 1$ 2. The derivative of sine: $\frac{d}{dx}sin(x) = cos(x)$ 3. The derivative of cosine: $\dfrac{d}{dx} \cos(x) = -\sin(x)$ -$$ \cos^2(x) = \frac{} +4. Half angle cosine identity: $\cos^2(x) = \frac{1}{2}(1 + \cos(2x))$ +5. Half angle sine identity: $\sin^2(x) = \frac{1}{2}(1 - \cos(2x))$ +6. $tan^2(x) + 1 = sec^2(x) \Rightarrow \int \sec^2(x)$ +7. $\dfrac{d}{dx}(\tan(x)) = \sec^2(x)$ +8. +