The oestrogen provided in the BCP (birth control pill) may be enough to control menopausal symptoms if you happened to be going through it whilst on birth control pills so in a way yes it could mask the fact that you were going through the menopause (depending on the level of oestrogen you are on) . Having said that, the night sweats can be side fx of the pill.
With regards to periods, the bcp causes a monthly period so there is no reason why that would necessarily stop because you may be going through an early menopause. They would stop however, if you were definitely going through menopause and not on the bcp!

If you are concerned and really want to know then a trip to the Doc to check your hormone levels esp FSH (follicle stimulating hormone) and LH ( lutenizing hormone) (used to determine if you are in or about to enter menopause) would be best but am not sure if they can test that if still on the bcp, but I’m sure they’ll clarify that for you!

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No,It could be the affect from the pill.Did you stop your period?I would go get it check out by your doctor.The doctor would know.

No, the pill will not affect menopause. The pill does regulate periods, but it will not cause your body to continue to have them after menopause has begun.