Consider LHS:
Simplify using half angle formula.
[tex] \frac{ \sin {}^{2} (x) - \cos {}^{2} (x) }{ \sin(x) - \cos(x) } = \sin(x) + \cos(x) [/tex]
Divide LHS
[tex] \sin(x) + \cos(x) = \sin(x) + \cos(x) [/tex]
