PWM frequency and LC filter
So what is the PWM frequency will output?


If your triangle wave is 2 kHz then the output PWM frequency is 2 kHz: -




  After getting the PWM signal filters I want to get a sinusoid, using
  an LC filter, but do not know what the frequency of cut should I use?


Well an LC low pass filter has a cut-off frequency defined by: -

F = \$\dfrac{1}{2\pi\sqrt{LC}}\$

But, it's also a series resonant circuit so if you run either your 50 Hz or 2 kHz anywhere near that resonant point you are going to get rather large currents and, as has been mentioned in a comment a good starting point is the geometric mean i.e. 316 Hz. If you felt that the output ripple voltage (2kHz ripple) superimposed on the 50 Hz was too high you could lower the filter frequency towards 100 Hz but I'd probably use a simulator to see what the likely impact of this is. Alternatively I'd consider rasing the 2 kHz to maybe 10 kHz or higher.