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Home » Question: Compute $ \cos 180^\circ $. - jntua results

Question: Compute $ \cos 180^\circ $. - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 rac{N^3 - 3ND^2}{D(N^2 + D^2)} = x

📌 Multiply both sides by \( D(N^2 + D^2) \):

📌 N^3 - 3ND^2 = x D (N^2 + D^2)

📌 Now substitute back \( N = x^3 - 3x \), \( D = x^2 + 1 \):

📌 \( N^2 = (x^3 - 3x)^2 = x^6 - 6x^4 + 9x^2 \)

📌 \( N^3 = (x^3 - 3x)^3 = x^9 - 9x^7 + 27x^5 - 27x^3 \)

📌 \( D^2 = (x^2 + 1)^2 = x^4 + 2x^2 + 1 \)

📌 \( N^2 + D^2 = x^6 - 6x^4 + 9x^2 + x^4 + 2x^2 + 1 = x^6 - 5x^4 + 11x^2 + 1 \)

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