Professors shows poor understanding of material

Uh, you should file a complaint, and encourage your peers to do so as well. There was this lecturer we had that was just... bad, so half of the students in that year filed a complaint. They changed him the following year. I don't think you can get any money back though, no. Just have to study them all yourself.
This year we have a professor who is on strike for more than half of the lectures. Yikes. Professor quality is something we can only hope for...

So this professor's lecture slides in engineering, he provides examples and then says things like "It is obvious that the result is ..." Hes essentially just making statement without saying why and says its obvious or he'll say a something condescending like 'A quick test of your trigonometry will show this'

So this is “Professor code” for one of the following .

1) "The maths you need here is basic and dull and you should know this stuff from A levels / last term’s course. I could teach it to you (again) but that just gets in the way of the new stuff I need to give you for this course".

OR

2) "Well done, you have noticed a tricky bit. It will appear on a problem sheet and then on the exam, so students who work out how to do this get a decent pass"

OR

3) “I don’t know how to do this stuff”.

Its never 3. There are many brutal hurdles to get over to be able to progress from undergrad through masters, PhD, Post Doc, Research Fellow, Lecturer, Reader to Prof so if its engineering, there is zero probability its this.

How are we suppose to improve the thinking of the next generation with these professor's?
Someone has to complain to higher authority to make some changes, its terrible for the country

You can't "get your money back", no. That's not how it works.

If this is a consistent problem then raise it with your department / student rep to see if it can be improved. Otherwise there's not really much to be done. Making grand statements like this is not going to help you particularly either. Focus on what can be improved about your course not on the value of your course to wider society.

But are my statements wrong?
Could you explain how the next generation will improve if the current teaching is sub standard?

No i would disagree, Engineers should never be teaching Mathematics concepts because their understanding of those concepts revolve mainly around concrete example whereas the concepts themselves are abstract

Much of an engineering degree is inherently mathematical, it’s just the tool you use to solve problems that need a numerical answer. You don’t need a mathematics Prof to do that if the skill set required is well within the competence of any professional engineer. Yes, there are times to get a dedicated maths lecturer in (number theory anyone ) but “basic trig” as needed for the example here really does not come under that category.

I sometimes teach mathematical bits of a course myself while not being a “professional mathematician”. My focus is on the “new stuff” specific to that course, I still expect students to be able to all the underpinning “boring” stuff without holding their hand through basic trig and similar.

It was not just basic trigonometry to prove the statement given by the professor
The prove actually extends deeply into mathematical set theory and vector analysis, yet he provided a basic diagram with no labels and says 'Quick test of your trigonometry shows this result'
Is he deluded or he doesnt understand the Mathematics he applying at a deeper level than just a concrete application?

What are the chances this will happen?

Ok, so this looks like a “Type 2 Problem”. It turns out to be non trivial and you found that out by digging into how to solve it. Well done, you get to progress to the next level and nail it if it comes up in the exam.

It’s entirely appropriate on a decent STEM degree that your Profs drop this kind of problem on you. At some point you are going to have to take ownership of a safety critical calculation as a professional engineer, do that with zero hand holding, and stand by the answer, possibly in a court of law. THIS is how you get to develop the required skill set.

No buddy, he doesn't understand Mathematics at a deeper level thats his problem
He understands Mathematics only as a concrete application relevant to his field, he even claims himself in the lecture slides that he isnt a Mathematician

But do you understand the problem better now having gone through it like this ...... it seems so. That's the required outcome, along with a broader appreciation of the whole problem solving process, so you may be p***ed, but the Prof "wins" in terms of delivering improved student understanding .

The type of guy who "Creates problems for others" to claim "Its for your own benefit buddy"

Oh yeah, the good ol condescending statement
Because 'Youre less than me' then i dont need to do this
Get a grip mate, im asking you for the answer to that question