tanx/2=1/2求sin(x+π/6)

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tanx/2=1/2求sin(x+π/6)

tanx/2=1/2求sin(x+π/6)
tanx/2=1/2求sin(x+π/6)

tanx/2=1/2求sin(x+π/6)
tan(x/2)=1/2,sinx=2tan(x/2)/[1+tan²(x/2)]=4/5,
cosx=[1-tan²(x/2)]/[1+tan²(x/2)]=3/5,
sin(x+π/6)=sinxcos(π/6)+cosxsin(π/6)=4/5*√(3)/2+3/5*1/2=[3+4√(3)]/10

sin(x π/6) (sin2x sin^2x)/(1-cos2x) =sin(x π/6)(2sinxcosx sin^2x)/2sin^2x =[1/2 cosx/sinx]sin(x π/6) =[1/2 1/tanx]