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Home » \[ 2(1 - \sin^2 \theta) - 3\sin \theta = 0 \] - Appfinity Technologies

\[ 2(1 - \sin^2 \theta) - 3\sin \theta = 0 \] - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 $ \left(\frac{79}{160}\right)^5 = \frac{79^5}{160^5} $, but instead, accept the decomposition:

📌 c_3 = \frac{79}{160} - \frac{1}{5} \cdot \left(\frac{79}{160}\right)^5

📌 But since the fifth power is not a perfect fifth, and given the model context, we proceed symbolically:

📌 Let $ u = \frac{79}{160} $. Then $ c_3 = u - \frac{u^5}{5} $. This is exact, but we compute numerically for final boxed value as expected in olympiad context with simplification.

📌 Instead, recheck: perhaps the recurrence allows exact subtraction. But due to complexity, we evaluate:

📌 Using calculator-assisted simplification (as allowed in reasoning),

📌 $ \left(\frac{79}{160}\right)^5 \approx 0.0935 $, so $ \frac{1}{5} \times 0.0935 \approx 0.0187 $,

📌 $ c_3 \approx 0.49375 - 0.0187 = 0.47505 $, but we seek exact form.

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