Cosine: Deriving the formula for Cosine of the Sum of two angles: http://www.youtube.com/watch?v=ObaA-rYHO9o
Sine: Uses the formula for the cosine of the sum of two angles to derive the formulas for the cosine of the difference of two angles, the sine of the sum of two angles, and the sine of the difference of two angles. Examples using the formula are provided: http://www.youtube.com/watch?v=B9nWZWIN8_I
Tangent: This video derives the identity for the tangent of the sum and difference of angles (or real numbers), and provides an example using the identity if you know the tangents of two angles, but not their sum: http://youtu.be/dCcelh6Jkng