- #1

fredrick08

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- 0

## Homework Statement

use the definitions of the trig functions in terms of complex exponential to prove:

cos([tex]\theta[/tex]/2)=[tex]\pm[/tex]sqrt(1+cos([tex]\theta[/tex])/2) and

sin([tex]\theta[/tex]/2)=[tex]\pm[/tex]sqrt(1-cos([tex]\theta[/tex])/2)

## Homework Equations

e^i[tex]\theta[/tex]=cos[tex]\theta[/tex]+isin[tex]\theta[/tex]

e^-i[tex]\theta[/tex]=cos[tex]\theta[/tex]-isin[tex]\theta[/tex]

cos[tex]\theta[/tex]=1/2(e^i[tex]\theta[/tex]+e^-i[tex]\theta[/tex])

sin[tex]\theta[/tex]=1/2i(e^i[tex]\theta[/tex]+e^-i[tex]\theta[/tex])

## The Attempt at a Solution

Ok im just not sure where to start with this one... my answer obviously has a sqrt in it, and also cos[tex]\theta[/tex]... do i need cos^2[tex]\theta[/tex]+sin^2[tex]\theta[/tex]=1?

or sin2[tex]\theta[/tex]=2sin[tex]\theta[/tex]*cos[tex]\theta[/tex]?

But im unsure how the question wants to be done? it says use complex exponetials?? plz can anyone put me on the right track?