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Home » \( 2a = 13.85 \) → \( a = 6.925 \) - RTA

\( 2a = 13.85 \) → \( a = 6.925 \) - RTA

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 Group the first and last terms:

📌 f(\theta) = (\sin^4 \theta + \cos^4 \theta) - 4\sin^2 \theta \cos^2 \theta.

📌 Recall that:

📌 \sin^4 \theta + \cos^4 \theta = (\sin^2 \theta + \cos^2 \theta)^2 - 2\sin^2 \theta \cos^2 \theta = 1 - 2\sin^2 \theta \cos^2 \theta.

📌 Substitute into $ f(\theta) $:

📌 f(\theta) = (1 - 2\sin^2 \theta \cos^2 \theta) - 4\sin^2 \theta \cos^2 \theta = 1 - 6\sin^2 \theta \cos^2 \theta.

📌 Now use the identity $ \sin(2\theta) = 2\sin\theta \cos\theta $, so:

📌 \sin^2(2\theta) = 4\sin^2\theta \cos^2\theta \Rightarrow \sin^2\theta \cos^2\theta = \frac{1}{4} \sin^2(2\theta).

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