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prove the pythagorean theorem.
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the pythagorean theorem states that for any right triangle with legs 'a' and 'b' and hypotenuse 'c', a² + b² = c². this can be proven using the law of cosine, where the angle opposite of leg 'c' is 90 degrees, yielding c² = a² + b² - 2ab cos(90). plugging in 90 to cos(90) gives us c² = a² + b², thus proving the pythagorean theorem.
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