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- \(2\sin A \cos B = \sin(A + B) + \sin(A - B)\)
- \(2\cos A \sin B = \sin(A + B) - \sin(A - B)\)
- \(2\cos A \cos B = \cos(A + B) + \cos(A - B)\)
- \(2\sin A \sin B = \cos(A - B) - \cos(A + B)\)
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- \(\sin(A + B)\sin(A - B) = \sin^2 A - \sin^2 B = \cos^2 B - \cos^2 A\)
- \(\cos(A + B)\cos(A - B) = \cos^2 A - \sin^2 B = \cos^2 B - \sin^2 A\)
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- \(\sin C + \sin D = 2\sin\frac{C + D}{2} \cos\frac{C - D}{2}\)
- \(\sin C - \sin D = 2\cos\frac{C + D}{2} \sin\frac{C - D}{2}\)
- \(\cos C + \cos D = 2\cos\frac{C + D}{2} \cos\frac{C - D}{2}\)
- \(\cos C - \cos D = 2\sin\frac{C + D}{2} \sin\frac{D - C}{2}\)