I making math problem solving fun (for me)

[Hamiltonian]

I love physics and I know it's quite hypocritical to say that I don't enjoy math that much.

I started studying classical mechanics at the beginning of the previous year, all problems were amazingly fun to solve and could be related to the real world very easily, obviously, I had to get a good grip on single variable calculus and basics of vectors to understand the subject properly, hence naturally I grew interested in calculus!

but when I solve problems in topics like trigonometry or sequence and series most questions require clever manipulations to reach a final answer and many a time I think what's the point of landing at a solution after so much hard work when I could have just used a calculator or that I would never encounter something so difficult in the real world. Sometimes the manipulations needed to be done are quite elegant but I still don't think they are worth the hassle. (even coordinate geometry gets quite fiddly sometimes)

The questions we are given at school(as assignments) have difficulty below the level of math olympiads but are focused only on solving problems for university entrance exams and due to this most questions we are given are bland(although difficult).

I want help in making solving "boring"(I know it's subjective) but difficult problems fun!

(i attached a few problems as an example of what I am talking about)

 

[Choppy]

While not everything in life is going to be fun, I suppose there's a point in making the effort to try and enjoy the less fun elements as much as you can.

If you're the kind of person who finds problems more interesting when you can connect them with a real world application, then at the risk of stating the obvious, it's worth spending some time when you review your material to make those real world connections yourself. Spend some time reading beyond what's assigned and look for how these concepts are applied, or more importantly, how you can apply them in scenarios that interest you.

Something else to keep in mind too is that the point of a lot of mathematical exercises is to develop skill. Remember there's a difference between knowledge and skill. I can explain to you how an internal combustion engine works, but I still gladly take my car to a mechanic when it needs any work beyond some very basic stuff. I could still do the work, but for me to change brake pads, for example, would take me a very long time compared to a mechanic because the mechanic is much more skilled than I am. In math you develop those skills through practice solving lots of problems.