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来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/23 02:06:42
已知0已知0已知0由tan(x/2)+cot(x/2)=5/2则:sin(x/2)/cos(x/2)+cos(x/2)/sin(x/2)=5/2[sin^2(x/2)+cos^2(x/2)]/[sin
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由tan(x/2)+cot(x/2)=5/2
则:
sin(x/2)/cos(x/2)+cos(x/2)/sin(x/2)=5/2
[sin^2(x/2)+cos^2(x/2)]/[sin(x/2)cos(x/2)]=5/2
2/[2sin(x/2)cos(x/2)=5/2
2/sin(x)=5/2
5sin(x)=4
sin(x)=4/5
由于0 0
则:cos(x)=根号[1-sin^2(x)]
=3/5
则:sin(x-Л/3)
=sinxcospi/3-sinpi/3cosx
=4/5*1/2-根号3/2*3/5
=(4-3根号3)/10
由tan x/2 + cot a/2 = 5/2切化弦
求出SINX=4/5
又
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代入公式得
SIN(x-Л/3)=(4-3*根号3)／10