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Double-angle and compound-angle formulas
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Learn it sin 2θ = 2 sin θ cos θ; cos 2θ = cos²θ − sin²θ = 1 − 2sin²θ = 2cos²θ − 1. Compound: sin(A ± B) = sin A cos B ± cos A sin B; cos(A ± B) = cos A cos B ∓ sin A sin B.
Example: If sin θ = 3/5 and θ is acute, find sin 2θ.
- cos θ = 4/5.
- sin 2θ = 2(3/5)(4/5) = 24/25.
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