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文1对常见不等式sinA/2sinB/2+sin/B2sinC/2+sinC/2sinA/2≤34进行了加强,并对其下界进行了估计,实际得到了如下结果:命题1在△ABC中,R,r分别为其外接圆和内切圆半径,则有3r/2R≤sinA/2sinB2+sinB/2sinC/2+sinC/2sinA/2≤1/2+r/2R.原文证明过程中利用半角公式把上述不等式转化成边的关系,并借助了几个三角恒等式和
In this paper, we strengthen the common inequalities sinA / 2sinB / 2 + sin / B2sinC / 2 + sinC / 2sinA / 2≤34 and estimate the lower bounds. The following results are obtained: Proposition 1 In △ ABC, R , r are respectively the circumcircle and inscribed circle radius, then 3r / 2R≤sinA / 2sinB2 + sinB / 2sinC / 2 + sinC / 2sinA / 2≤1 / 2 + r / 2R.The original proof process using the half-angle formula Transform these inequalities into side relations, with the help of several triangular identities