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设x1x2为x平方-(sinπ/5)x-cosπ/5的两根,则arctgx1+arctgx2的值为?
题目详情
设x1 x2为x平方-(sinπ/5)x-cosπ/5的两根,则arctgx1+arctgx2的值为?
▼优质解答
答案和解析
∵x1 x2为x平方-(sinπ/5)x-cosπ/5的两根
∴x1+x2=sinπ/5>0 x1x2=-cosπ/5<0
∴tg(arctgx1+arctgx2)=(x1+x2)/(1-x1x2)=(sinπ/5)/(1+cosπ/5)=tgπ/10
∴arctgx1+arctgx2=π/10
∴x1+x2=sinπ/5>0 x1x2=-cosπ/5<0
∴tg(arctgx1+arctgx2)=(x1+x2)/(1-x1x2)=(sinπ/5)/(1+cosπ/5)=tgπ/10
∴arctgx1+arctgx2=π/10
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