How would you prove sin2x+cos2x=1 using Euler's formula?
eix=cos(x)+isin(x)
This is what I have so far:
sin(x)=12i(eix−e−ix)
cos(x)=12(eix+e−ix)
Answer
Multiply eix=cos(x)+isin(x) by the conjugate identity ¯eix=cos(x)−isin(x) and use that ¯eix=e−ix hence eix⋅¯eix=eix−ix=1.
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