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education/math/MATH1220 (calc II)/Integration with Trig Identities.md
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@ -2,4 +2,9 @@ The below integration makes use of the following trig identities:
1. The Pythagorean identity: $\sin^2(x) + \cos^2(x) = 1$ 1. The Pythagorean identity: $\sin^2(x) + \cos^2(x) = 1$
2. The derivative of sine: $\frac{d}{dx}sin(x) = cos(x)$ 2. The derivative of sine: $\frac{d}{dx}sin(x) = cos(x)$
3. The derivative of cosine: $\dfrac{d}{dx} \cos(x) = -\sin(x)$ 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.