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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. 
+