How can i understand and prove the sum and difference formulas in trigonometry – Artofit

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How can I understand and prove the "sum and difference formulas" in trigonometry
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$Picture/intuitive proof of $\cos(3 \theta) = 4 \cos^3(\theta)-3\cos(\theta)$?$

Picture/intuitive proof of $\cos(3 \theta) = 4 \cos^3(\theta)-3\cos(\theta)$?

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