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