In the study of transistor as an amplifier, if α = Ic/Ie and β = Ic/Ie, where lc, lb and le are the collector, base and emitter currents, then
β=1-αα
β=α1-α
β=α1+α
β=1+αα
As we know iE=iC+iB
⇒ieic=1+ibic⇒1α=1+1β⇒β=α1-α