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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)

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)

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