How To Find The Sin(A+B)=SinA.CosB+CosA.SinB?

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The equation Sin(A+B) = SinA.CosB + CosA.SinB can be derived using Euler's formula, which states e^{ix} = cos(x) + i sin(x). By substituting A+B for x and expanding the expression, one can separate the real and imaginary components. This method provides a clear and straightforward proof of the identity. Understanding this derivation enhances comprehension of trigonometric functions and their relationships. The discussion emphasizes the utility of Euler's formula in trigonometry.
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Hi everyone,

I wonder why Sin(A+B)=SinA.CosB+CosA.SinB?

Huygen
 
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The easiest way to see this is to use Euler's formula:
e^{ix} = cos(x) + i sin(x)

put in A+B for x, expand it, and collect real and imaginary parts.
 

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