1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Apply a corollary to show an identity

  1. Feb 21, 2015 #1
    1. The problem statement, all variables and given/known data

    Apply corollary to show that 2 sinz*sinw = cos(z-w) - cos(z+w) for any z,w ∈ ℂ

    2. Relevant equations

    2 sinz*sinw = cos(z-w) - cos(z+w) for any z,w ∈ ℂ

    Corollary: Let f and g be analytic functions defined on a domain D ⊂ ℂ. Let E ⊂ D be a subset that has at least one limit point a in D. If f|E = g|E, then f = g in D.

    3. The attempt at a solution

    Of course, this trig identity holds in both the real and complex spaces. As I understand it, the notation f|E means that f is restricted to the subset E. I'm not sure if it's as easy as simply plugging in two values from E and then claiming that the functions are equal and then extending that to the larger domain D.
     
  2. jcsd
  3. Feb 21, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Two values are not enough, the identity has to hold for every point in E in order to use the corollary - but you have the freedom to choose E as long as it satisfies the condition with the limit point.

    I guess you are allowed to use the standard trigonometric identities for real numbers here.
     
  4. Feb 21, 2015 #3
    Yeah, I guess I'll simply use the Angle-Sum and -Difference Identities.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Apply a corollary to show an identity
Loading...