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please-prove-A-B-C-are-angles-of-triangle-cylic-sinA-sinB-cosc-8cos-A-2-cos-B-2-cos-C-2-




Question Number 107624 by mnjuly1970 last updated on 11/Aug/20
       please prove:   A,B,C  are angles of  triangle.  Σ_(cylic) ((sinA+sinB)/(cosc))≥8cos(A/2)cos(B/2)cos(C/2)
$$\:\:\:\:\:\:\:{please}\:{prove}: \\ $$$$\:\mathrm{A},\mathrm{B},{C}\:\:{are}\:{angles}\:{of} \\ $$$${triangle}. \\ $$$$\underset{{cylic}} {\sum}\frac{{sinA}+{sinB}}{{cosc}}\geqslant\mathrm{8}{cos}\frac{{A}}{\mathrm{2}}{cos}\frac{{B}}{\mathrm{2}}{cos}\frac{{C}}{\mathrm{2}}\:\:\:\:\:\:\: \\ $$$$ \\ $$

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