Let △ A B C be an acute-angled triangle. Prove that ∑ cyc cot ⁡ A + cot ⁡ B ≥ 2 2

Question

Let   △  A  B  C be an acute-angled triangle. Prove that       ∑    cyc        cot    ⁡          A        +    cot    ⁡          B        ≥  2      2

last99erib · Accepted Answer

hint:      cot    ⁡          A        +    cot    ⁡          B        =                              s          i          n          (          A          +          B          )                          s          i          n          A          s          i          n          B                      =                              s          i          n          C                          s          i          n          A          s          i          n          B                      =                    s        i        n        C                    s        i        n        A        s        i        n        B        s        i        n        C              3            s      i      n      A      s      i      n      B      s      i      n      C        3    ≤  s  i  n  A  +  s  i  n  B  +  s  i  n  C  ≤                    3                  3                    2

Let <mi mathvariant="normal">△ A B C be an acute-angled triangle. Pr

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