How much time trigonometry will take of JEE syllabus for completion?
Generally it takes 3-4 weeks to complete trigonometry of JEE syllabus. Even if you study day and night, it will take a minimum of 10-15 days to have some kind of grip on JEE trigonometry. In order to master trigonometry, a considerable practice is required which would take time.
Learn all the formulas first, do basic questions and then important/ JEE previous years questions. It is advised to not rush through trigonometry as about half of the calculus questions are based on trigonometric identities and related manipulations.
Keep in mind that learning a topic in JEE depends on your IQ, concentration, focus and other factors - whether it takes a week or a month.