Recent content by Heisenberg7

I am using those at the moment. I suppose I am on their level, but I am looking for something to upgrade to after completing the intermediate versions.

Hello, I am looking for contest math books, problem sets, videos, etc. I'm quite good at algebra, but I'm not so good at geometry, counting, probability and number theory. I know a few resources such as aops, AMC, AIME, local competitions and a few books. It would be great if you could suggest...

Thank you for motivating me. Eh, where would this world be without people like you or @fresh_42 who are always there to help others!

Indeed. But, I simply can't help but wonder how an average high school student would find this if they hadn't played with the fraction for at least an hour(religiously), without knowing the result. I worked on this for quite a while, but still couldn't find the result. I felt kind of...

Thank you, @PeroK and @fresh_42 for trying to help! I would like to present the solution from my book. Here it is: It's quite elegant really. But you must play with ##\frac{\cos{kx}}{\cos^{k}{x}}## for quite a while to get to the result.

It was probably a mistake to post it here instead of posting it in the precalc section.

Thank you for you response. This is definitely WAY above my level of understanding. This is listed as a high school level problem, so I expected some high school stuff, but it turns out this could involve some advanced mathematics. Pretty interesting!

Greetings, I would like to gain some insight when it comes to dealing with this problem. Personally, I wasn't able to solve it. I had to look for the solution in the book. I can just tell you that it's a telescopic series, the rest would be too much. You don't have to post the whole solution...

Thank you for your response. I suppose this was more of a self esteem problem, but there certainly are some ways I can improve the final result (read my reply above).

Thank you for your response. Your story is simply fantastic and your writing is so fine. I really had to compliment you on that. I will definitely try to dedicate some time into watching that anime of yours. Anyway, I have watched a few lessons on psychology and thinking by Jordan B. Peterson...

Also, I can clearly see that something is wrong in my way of thinking, when my classmates who work 15 times less than me often see things before me.

Thank you for your response. Yes, I agree with you. I followed that path 99% of the time. And, to be honest, it worked 90% of the time. But, this 10% is making me a huge problem. Our professor is planning to give us problems that we've possibly never seen. And, whenever I have to do a new tough...

By the way, here is the problem: Prove that for a sharp angle ##\alpha## this inequality holds: $$\sqrt{\sin{\alpha}}\sqrt[4]{\tan{\alpha}} + \sqrt{\cos{\alpha}}\sqrt[4]{\cot{\alpha}} \geq \sqrt[4]{8}$$

Hello, This month, I've solved around 700 problems in trigonometry. And, I probably went over 200 problems again to internalize a few concepts, but I still have that feeling that I'm missing something. Last week, I was practicing math in cafeteria (early in the morning) and my math professor...

Here's a list: -Permutations and Combinations -The Pigeonhole Principle -Generating Permutations and Combinations -The Binomial Coefficients -The Inclusion-Exclusion Principle and Applications -Recurrence Relations and Generating Functions -Special Counting Sequences -Combinatorial Designs