- #1

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## Homework Statement

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

## Homework 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.

## 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.