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education/math/MATH1220 (calc II)/Integration with Trig Identities.md

@@ -58,10 +58,20 @@ $$ \int\frac{3}{4+x^2}dx = \frac{3}{2}\arctan(\frac{x}{2}) + C $$
 
 # A VERY LARGE LIST OF TRIG IDENTITIES FOR CALCULUS
 
-| non calc identities<br>              |
+| Reciprocal           |
 | ------------------------------------ |
 | $\csc(x) = \dfrac{1}{sin(x)}$        |
 | $\sec(x) = \dfrac{1}{\cos(x)}$       |
 | $\cot(x) = \dfrac{1}{\tan(x)}$       |
-| $\tan(x) = \dfrac{\sin(x)}{\cos(x)}$ |
+
+| Quotient |
+| -- |
+| $\tan(x) = \dfrac{\sin(x)}{\cos(x)}$  |
+| $\cot(x) = \dfrac{\cos(x)}{\sin(x)}$  |
+
+| Pythagorean |
+| -- |
 | $\sin^2(x) + \cos^2(x) = 1$          |
+| $1 + \tan^2(x) = \sec^2(x)$          |
+| $1 + \cot^2(x) = \csc^2(x)$          |
+| $1