vault backup: 2024-10-21 09:43:49

education/math/MATH1060 (trig)/Identities.md

@@ -1,3 +1,4 @@
+An **identity** is an equation that is true for all values of the variable for which the expressions in the equation are defined.
 # Trigonometric Identities
 
 All of the following only apply when the denominator is not equal to zero.
@@ -63,4 +64,12 @@ $$ \frac{625}{625} - \frac{49}{625} = \frac{576}{625} = sin^2\theta $$
 Getting rid of the exponent:
 $$ \sqrt{\frac{576}{625}} = \frac{24}{25} = sin\theta $$
 
-From there, you can find the rest of the identities fairly easily.
+From there, you can find the rest of the identities fairly easily.
+
+# Simplifying trig expressions using identities
+Given the difference of square formula:
+$$ a^2 - b^2 = (a-b)(a+b) $$
+
+## Examples
+Simplify $\tan\theta\sin\theta + \cos\theta$:
+1. $\frac{\tan\theta\sin\theta}{\sin\theta} + \frac{cos\theta}\frac{sin\}