Why is it important to learn how to prove trig identities (and similar mathematical statements like in Geometry)?

Proofs are the basis of mathematics. Math is really all about proving things. When you get into higher-level mathematics, proofs will be most of what you do.

Well you always learn how to prove everything in math. You can't rely on someone telling you something and hoping it's right. You need to show it. Proving things later on doesn't become important because everyone has gone through that process of learning it and people will not argue against you unless doesn't believe you

(By higher-level here I mean undergraduate and graduate-level mathematics. Not everyone gets to that point.)

it improves your critical thinking..which is crucial in later maths

Kinda the same way when people don't ask you to prove integral later on because proving can be tedious and unless the person doesn't know it, proving will seem a waste of a time,

But you always need to learn them.

Actually, when you get into higher-level mathematics, proof-writing becomes your major focus. Computing answers to problems is often not so hard, the harder part is proving theorems, and that is also the part that is most useful to a pure mathematician. Proving theorems is really the work that a pure mathematician does.

Thank you everyone :)

@nbouscal Yeah you are so right. I'm saying this from the point of view of an engineer. The highest level of math I had to take is Linear Algebra and although that level of math does require a great amount of proofs, for the most part I deal with math that becomes repetitive. I'm sure that other upper level courses require a lot of proofs.

Yes, engineering and sciences do not require as much emphasis on proofs because they are applied maths. Proofs are really key in pure maths.

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