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设sin(θ/2)-cos(θ/2)=3/√5.且180°
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设sin(θ/2)-cos(θ/2)=3/√5.且180°
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答案和解析
sin(θ/2)-cos(θ/2)=3/√5
2sin(θ/4)cos(θ/4)-[cos^2(θ/4)-sin^2(θ/4)]=(cos^2(θ/4)+sin^2(θ/4))3/√5
两边同除以cos^2(θ/4),为好写,记tanθ/4 =x
则2x-1+x^2=3/√5+(3/√5)x^2,(3-√5)x^2-2√5 x+3+√5=0
x1=(√5+1)/(3-√5)=√5+2,
x2=(√5-1)/(3-√5)=(√5+1)/2
180°x1舍去,x2是所求的解
2sin(θ/4)cos(θ/4)-[cos^2(θ/4)-sin^2(θ/4)]=(cos^2(θ/4)+sin^2(θ/4))3/√5
两边同除以cos^2(θ/4),为好写,记tanθ/4 =x
则2x-1+x^2=3/√5+(3/√5)x^2,(3-√5)x^2-2√5 x+3+√5=0
x1=(√5+1)/(3-√5)=√5+2,
x2=(√5-1)/(3-√5)=(√5+1)/2
180°x1舍去,x2是所求的解
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