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230问答网 > 已知△ABC的面积S=(b+c)눀-a눀，则tan(A⼀2)的值为

已知△ABC的面积S=(b+c)눀-a눀，则tan(A⼀2)的值为

2025-03-31 17:04:59

推荐回答（1个）

回答1：

解：∵S=1/2*bcsinA=b^2+c^2+2bc-a^2

化简整理得cosA+1=1/4sinA···· ① cosA^2+sinA^2=1·····②

由①②解得cosA=-15/17 ∴sinA=8/17 即tanA=-8/15

∴2tanA/2/1-tanA/2^2=-8/15 解得tanA/2=4

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