Question

Using exp(iθ) = cos(θ)+ i sin(θ), show that
cos^2(θ) + sin(θ) = 1

Answer 1

You mean \( \sin^2(\theta)\)

Answer 2

^Yes, sorry!

Answer 3

It is easy
\[
e^{i \theta} = \cos(\theta) + i \sin(\theta)\\
e^{-i \theta} = \cos(\theta) - i \sin(\theta)\\

\]

Answer 4

Multiply the two equations and you are done

Answer 5

\[
e^{i \theta} = \cos(\theta) + i \sin(\theta)\\
e^{-i \theta} = \cos(\theta) - i \sin(\theta)\\

1= e^{i \theta} e^{-i \theta} = \cos^2(\theta) -(i \sin(\theta)^2=\cos^2(\theta)+\sin^2(\theta)
\]

Answer 6

Did you understand it?

Answer 7

ohh I see
Oh my yes thank you !! :)

Answer 8

YW