No, the time of sunset at the equator does not remain the same every day. The equator experiences relatively consistent day and night lengths throughout the year, but the actual time of sunset can vary.
The duration of daylight at the equator is approximately 12 hours throughout the year, given that the equator is located halfway between the poles where the tilt of the Earth's axis has less impact on day and night lengths. However, the specific time of sunset can still vary due to factors such as the Earth's axial tilt and the observer's position within the time zone.
The Earth's axial tilt, approximately 23.5 degrees, causes the position of the Sun relative to the observer to change throughout the year. This tilt results in the Sun's apparent path in the sky shifting between the Tropic of Cancer (23.5 degrees north of the equator) during the June solstice and the Tropic of Capricorn (23.5 degrees south of the equator) during the December solstice.
As a result, the time of sunset at the equator can vary slightly throughout the year, as the Sun's position changes. Additionally, the specific time of sunset can be influenced by the observer's position within their time zone, local atmospheric conditions, and other factors that can affect the visibility of the Sun.
Therefore, while the equator generally experiences equal day and night lengths, the exact time of sunset can still vary from day to day.