tan(α+π/4)=-3 ..用公式拆开
(tanα+tanπ)/(1-tanαtanπ)=-3
(tanα+1)/(1-tanα)=-3
-3+3tanα-tanα-1=0
2tanα=4
tanα=2
sin(2α-π/3) ..用公式拆开
=sin2αcosπ/3-cos2αsinπ/3
=0.5sin2α-√3/2cos2α
用万能公式,化得
=0.5*[2+tan(2α/2)]/[(1+tan(2α/2)^2]-(√3/2)*{[1-tan(2α/2)^2]/[1+tan(2α/2)^2]} ..约分
=0.5*(2+tanα)/[1+(tanα)^2]-(√3/2)*(1-(tanα)^2)/[1+(tanα)^2] ..代入tanα=2
=0.4+(3√3)/10
=(4+3√3)/10
约等于0.919615...