Proved as follows:

The crest factor of sine wave is √2. Assuming that the peak of sine wave is √2, its effective value is 1.

Suppose the signal period is t, the first T/2 is half wave, the last T/2 is zero, the effective value of the part that is not equal to zero is 1, the effective value of the part that is equal to zero is 0, and the effective value in a period t is √ ((12+02)/2) =1√ 2.

Crest factor = √ 2/(1√ 2) = 2.