已知tan(α+π/4)=-1/7.求(cos2α+1)/【2cos(α-π/4)*sin(α+π/4)-sin2α】的值.

问题描述:

已知tan(α+π/4)=-1/7.求(cos2α+1)/【2cos(α-π/4)*sin(α+π/4)-sin2α】的值.

tan(α+π/4)=(tanα+tanπ/4)/(1-tanα*tanπ/4)=(tanα+1)/(1-tanα)=-1/7解得tanα=-4/3(cos2α+1)/【2cos(α-π/4)*sin(α+π/4)-sin2α】=2cos²α/[sin2α+sin(π/2)-sin2α]=2/(1+tan²α)=2/[1+(-...