已知1/(sin(120-x))+1/(sin(120+x))=√3,求cosx的值
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/11/06 08:49:47
已知1/(sin(120-x))+1/(sin(120+x))=√3,求cosx的值
√3
=1/sin(120-x)+1/sin(120+x)
=[sin(120-x)+sin(120+x)]/sin(120-x)sin(120+x)
=2sin120cosx/(-1/2(cos240-cos2x))
=2√3cosx/(cos2x+1/2)
cos2x+1/2=2cosx
2cos^2x-1/2=2cosx
4cos^2x-4cosx-1=0
cosx=(1±√2)/2
因为:cosx∈ [-1,1]
所以,cosx=(1-√2)/2
=1/sin(120-x)+1/sin(120+x)
=[sin(120-x)+sin(120+x)]/sin(120-x)sin(120+x)
=2sin120cosx/(-1/2(cos240-cos2x))
=2√3cosx/(cos2x+1/2)
cos2x+1/2=2cosx
2cos^2x-1/2=2cosx
4cos^2x-4cosx-1=0
cosx=(1±√2)/2
因为:cosx∈ [-1,1]
所以,cosx=(1-√2)/2
已知1/sin(120°-x)+1/sin(120°+x)=4根号3/3 求cosx的值
已知tanx=1/2,求sin x-cos x/2sinx+3cosx的值
1/sin(x-120)-1/sin(x+120)=4根号3/3,求cosx
已知sin^3x+cos^3x=1,求sinx+cosx的值与sin^4x+cos^4x的值
已知sin^4x+cos^4x=1,求sinx+cosx的值
已知sin^4x+cos^x=1,求sinx+cosx的值
已知sinx-cosx=1/2,求sin^4x+cos^4x的值
已知sinx+cosx=1/5,x属于(0,π),求cos^3 X-sin^3 X的值
已知tanx=1/2,求(sinx+3cosx)/(sinx+cosx)和sin^2x+sinxcosx+2的值
请帮忙解答一下 已知函数f(x)=2cosx*sin(x+π/3)-√3sin平方x+sinx*cosx 1 求函数f(
已知cosx=3/4,则sin(5x/2)/2sin(1/2x)-1/2的值是?
化简:1、sin(x-π/3)-cos(x+π/6)+√3cosx=?2、已知,sinα+sinβ=√2/2,求cosα