A Compound Trgonometric Inequality | International Mathematical Olympiad 1965 Problem 1

Поділитися
Вставка
  • Опубліковано 15 лис 2024

КОМЕНТАРІ • 26

  • @littlefermat
    @littlefermat 3 роки тому +7

    Old IMOs when inequalities used to appear quite often, unfortunately not anymore :-(
    Nice video!

  • @dennisdesormier6886
    @dennisdesormier6886 3 роки тому +1

    At 1:46, instead of giving up so soon, just look at the 8 cases of x in [0, π/4], [π/4, π/2], etc., which you looked at anyway. The problem simplifies big time.

    • @richardfredlund3802
      @richardfredlund3802 2 роки тому

      indeed @Dennis Desormier ...i was thinking similar. Not sure it would have been simpler than the solution presented though.

  • @tricky1785
    @tricky1785 Рік тому

    Nice

  • @chessdev5320
    @chessdev5320 3 роки тому +1

    I think Triangle Inequality can make this a lot easier.

  • @Dharmarajan-ct5ld
    @Dharmarajan-ct5ld 3 роки тому +3

    You made it unnecessarily lengthy, and complicated, i suppose. Shorter solution shall be uploaded in few hours . Don't mind

    • @jose4877
      @jose4877 3 роки тому +2

      @Rick Does Math He's right. This solution is unnecessarily lengthy and complicated.

    • @Dharmarajan-ct5ld
      @Dharmarajan-ct5ld 3 роки тому

      @Rick Does Math please give sometime. I will upload in my channel, in few hours

    • @Dharmarajan-ct5ld
      @Dharmarajan-ct5ld 3 роки тому

      @@jose4877 5 step solution comes soon

    • @Dharmarajan-ct5ld
      @Dharmarajan-ct5ld 3 роки тому

      @Rick Does Math 5 To 6 steps enough.

    • @Dharmarajan-ct5ld
      @Dharmarajan-ct5ld 3 роки тому

      @Rick Does Math 6 step solution uploaded now in my channel

  • @ayoubabid8783
    @ayoubabid8783 3 роки тому

    Hi i have problem for you
    Let M (1,2,3.......,n) and A=(a1,a2.a3..........,am ) in M such that m is a natural number #0
    And for any b in M there exist ai , aj in group A such that 1

  • @sgdufbaoaah8692
    @sgdufbaoaah8692 3 роки тому

    good

  • @רוןשמיר-צ4ד
    @רוןשמיר-צ4ד 3 роки тому

    easy to see

  • @ADITYA-by9ym
    @ADITYA-by9ym 3 роки тому

    very easy question

  • @МатематическийприветсАэрокоса

    Level of Russia school exam) enough easy

  • @Blabla0124
    @Blabla0124 3 роки тому +1

    Just draw the graph with desmos, that'll take care of business

  • @javaman1300
    @javaman1300 3 роки тому

    So hard

    • @chessdev5320
      @chessdev5320 3 роки тому

      just like your name 🙃

    • @javaman1300
      @javaman1300 3 роки тому

      @@chessdev5320 Why bro

    • @javaman1300
      @javaman1300 3 роки тому

      Thai name often long and hard to read

    • @chessdev5320
      @chessdev5320 3 роки тому

      @@javaman1300 Sorry! not to offend you

  • @br75857
    @br75857 4 місяці тому

    Bro change the background screen black. It will be good for our eyes