The subject of trigonometry is in geometry.
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Neither trigonometry nor any other subject can be used to prove questions. It may be possible to answer questions but that is another matter,
There are no hindrances. If you put your mind to it, any subject can be mastered.
The subject has not concluded: there are still aspects of it that can be developed so it is premature to talk about the conclusion of the subject.
No one in particular because trigonometry has evolved over thousands of years with many ancient and modern mathematicians making their own discoveries and contributions to the subject.
plane trigonometry spherical trigonometry