Why non sinusoidal signals are not used as carrier in modulation?

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non sine wave carrier would require greater bandwidth and sine wave carrier is used because it produces the least amount of harmonics.
 

Your question contains an assertion that is not true.
 

Simply because any non sinusoidal signal is broadened in frequency domain and attain larger bandwidth than needed. In addition such carriers would create high level harmincs that interfere with other frequencies.
 

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