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)
根据 公式 有
sinx=2tanx/2 /(1+tan²x/2)=4/5
cosx=(1-tan²x/2)/(1+tan²x/2)=3/5
sin(x+π/6)=sinxcosπ/6+cosxsinπ/6=(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]