Explanation
In this case, Excel extracts the month from the date in cell B6 as a number, and the month in the cell C6 as a number, then tests for equivalency using the equal sign. Both dates are in January, so the formula is solved as follows and returns TRUE.
=MONTH(B6)=MONTH(C6)
=1=1
=TRUE
Same month as today
If you need to test a date to see if has the same month as the current date (today), you can use this formula:
=MONTH(date)=MONTH(TODAY())
Same month and year
To test that a date is the same month and year is another date, you can use this clever formula proposed by reader Eric Kalin:
EOMONTH(date1,0)=EOMONTH(date2,0)
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