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

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SUMMARY

The equation Sin(A+B) = SinA.CosB + CosA.SinB is derived using Euler's formula, 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 to arrive at the sine addition formula. This method provides a clear and concise proof of the identity.

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optics.tech
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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:
[tex]e^{ix} = cos(x) + i sin(x)[/tex]

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

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