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My honors trig teacher junior year taught these to our class to help us remember the rules for sine, cosine, and tangent of a sum. They got on our nerves after about the second time singing them, but we remembered those identities for the test.

To the tune of "If you're happy and you know it clap your hands"
Oh, the sine goes sine cosine cosine sine
The sine goes sine cosine cosine sine
The sign's the same in the sine, but it switches in the cosine
The sine goes sine cosine cosine sine

The cosine goes cosine cosine sine sine
The cosine goes cosine cosine sine sine
The sign's the same in the sine, but it switches in the cosine
The cosine goes cosine cosine sine sine

To the tune of "Mexican Hat Dance"
Tan a tan a tan a
Plus tan b tan b tan b
All over all over all over
1 minus tan a times tan b

This is the sum of tangents
This is the sum of tangents
This is the sum of tangents
Unless tan a times tan b equals 1

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