The output tube takes a saw tooth waveform not a sine wave, though back a ways from the output it is not really a saw tooth signal....
If you don't want to own a scope then you at least ought to find someone who will let you use theirs. There are many issues that a TV can have that are exceedingly difficult to impossible to accurately diagnose without one. If you are lucky you may be able to buy one for 10$ in working order if you keep a look out. Some of the newer scopes can be surprisingly small.
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