Thursday, July 7, 2016

trigonometry - Proof of sin2x+cos2x=1 using Euler's Formula




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(eixeix)



cos(x)=12(eix+eix)



Answer



Multiply eix=cos(x)+isin(x) by the conjugate identity ¯eix=cos(x)isin(x) and use that ¯eix=eix hence eix¯eix=eixix=1.


No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f:AB and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...