Enter two angles to apply product-to-sum and sum-to-product identities
Angle A (degrees)
Angle B (degrees)
Result
sinA x sinB
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cosA x cosB
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sinA x cosB
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sinA + sinB
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Detailed Derivation
Product Identity Formulas
sinA sinB = (1/2)[cos(A-B) - cos(A+B)]
cosA cosB = (1/2)[cos(A-B) + cos(A+B)]
sinA cosB = (1/2)[sin(A+B) + sin(A-B)]
sinA + sinB = 2 sin((A+B)/2) cos((A-B)/2)
These identities convert between product and sum forms of trigonometric functions. They are essential tools for integration and equation solving.
⚠These identities work for angles in any quadrant. Results are computed using standard trigonometric evaluations.
What Are Trig Product Identities?
Trig product identities convert between products of sine/cosine and sums/differences. They are derived from the angle sum and difference formulas and are fundamental in calculus and signal processing.
Product to Sum
Converts multiplication to addition: sinA sinB = (1/2)[cos(A-B)-cos(A+B)]. Great for integration.
Sum to Product
Converts addition to multiplication: sinA+sinB = 2sin((A+B)/2)cos((A-B)/2). Useful for solving equations.
Signal Mixing
In AM radio, multiplying carrier and signal waves creates sum and difference frequencies. Product identities explain this.
Integration
Products like sin(mx)cos(nx) integrate easily after converting to sums using these identities.
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