已知cosx=3/5,x属于(0,π),求sin(x-π/6),tan(x-π/6)的值

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已知cosx=3/5,x属于(0,π),求sin(x-π/6),tan(x-π/6)的值
已知cosx=3/5,x属于(0,π),求sin(x-π/6),tan(x-π/6)的值

已知cosx=3/5,x属于(0,π),求sin(x-π/6),tan(x-π/6)的值


∵cosx>0
x属于(0,π)
∴x∈(0,π/2)
sinx=4/5
sin(x-π/6)
=sinxcosπ/6-cosxsinπ/6
=4/5*√3/2-3/5*1/2
=(-3+4√3)/10
tanx=sinx/cosx=4/3
tan(x-π/6)
=(tanx-tanπ/6)/(1+tanxtanπ/6)
=(48-25√3)/11