Happy Christmas: Is it Really True?

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George Keeling
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TL;DR
sine and cosine power trees
Two Christmas tree shaped diagrams with a star on top, each listing power-reduction formulas: left cos^n θ equals a sum of cos(kθ) terms over 2^n, right sin^n θ with alternating signs, ending in a 32 denominator, with holly decorations and Season's Greetings text.

Is this really true? It resembles the binomial theorem.
I've posted it twice which might be breaking rules. Happy Christmas PF.
 
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