What is the value of SinA+sinB=?

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Trigonometric identities involving sine functions are fundamental tools in mathematics, physics, and engineering. The sin A sin B formulas, also known as sum-to-product and product-to-sum identities, help simplify complex trigonometric expressions and solve various mathematical problems.

Sum-to-Product Formulas

Formula Name	Mathematical Expression	Explanation	When to Use
Sin A + Sin B Formula	sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2)	Converts sum of sines into product form	Simplifying expressions, solving equations, integration
Sin A - Sin B Formula	sin A - sin B = 2 cos((A+B)/2) sin((A-B)/2)	Converts difference of sines into product form	Solving trigonometric equations, proving identities

Product-to-Sum Formulas

Formula Name	Mathematical Expression	Explanation	When to Use
Sin A × Sin B Formula	sin A sin B = ½[cos(A-B) - cos(A+B)]	Converts product of sines into sum/difference of cosines	Integration, Fourier analysis, wave interference
Sin A × Cos B Formula	sin A cos B = ½[sin(A+B) + sin(A-B)]	Converts sine-cosine product into sum of sines	Solving complex trigonometric problems
Cos A × Sin B Formula	cos A sin B = ½[sin(A+B) - sin(A-B)]	Converts cosine-sine product into difference of sines	Physics applications, signal processing

Extended Formulas and Variations

Formula Type	Mathematical Expression	Description
Double Angle (Special Case)	sin 2A = 2 sin A cos A	When A = B in sin A cos B formula
Triple Sum Formula	sin A + sin B + sin C	Use pairwise application of sum formulas
General Product Formula	sin(nA) sin(mA)	Requires combination of basic formulas

What is the value of SinA+sinB=?

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