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Proof of The Law of Cosines

Law of Cosines: a² = b² + c² - 2 bc cos Θ

Proof

a² = (b sin Θ)² + (c - b cos(Θ))²

= b² sin ² Θ + c² - 2cbcos(Θ) + b ² cos ² Θ

= b² (sin ² Θ + cos ² Θ + c² - 2cbcos(Θ)

= b² * 1 + c² - 2cbcos(Θ)

= b² + c² - 2cbcos(Θ)

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