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education/math/MATH1060 (trig)/Double and Half Angle Identities.md

@@ -1,3 +1,7 @@
+To solve for a double or half angle identity:
+1. Draw a triangle
+2. Choose an identity to use
+3. Substitute into formula
 # Double Angle Identities
 Sine:
 $$ \sin(2\theta) = 2\sin\theta\cos\theta $$
@@ -20,4 +24,10 @@ $$ \sin(\frac{\theta}{2}) = \pm\sqrt{\frac{1-\cos\theta}{2}} $$
 Cosine:
 $$ \cos(\frac{\theta}{2}) = \pm \sqrt{\frac{1 + \cos\theta}{2}} $$
 Tangent:
-$$ \tan(\frac{\theta}{2}) = \pm\sqrt{\frac{1-\cos\theta}{1 + \cos\theta}} $$
+$$
+\begin{matrix}
+\tan(\dfrac{\theta}{2}) = \pm\sqrt{\dfrac{1-\cos\theta}{1 + \cos\theta}}\\
+= \dfrac{\sin\theta}{1 + \cos\theta}\\
+= \dfrac{1 - cos\theta}{\sin\theta}
+\end{matrix}
+$$