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Verify the trigonometric formula for sin(a+b)=sinacosb+sinbcosa and cos(a+b)=cosacosb-sinasinb by using complex representation.

I tried to use Euler's formula to start but I am unsure how to use complex representation for this.

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Hint

Notice that $\sin(a+b)$ is the imaginary part of $$e^{i(a+b)}=e^{ia}e^{ib}=(\cos a+i\sin a)(\cos b+i\sin b)$$

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$$e^{i(a+b)}=e^{ia}\cdot e^{ib}$$

$$\cos(a+b)+i\sin(a+b)=(\cos a+i\sin a)(\cos b+i\sin b)$$

Multiply out the RHS & equate the real & the imaginary parts

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