tan(π/4-α)=-1/3 则sin(2α+π/4)的值为?
问题描述：
tan(π/4-α)=-1/3 则sin(2α+π/4)的值为?
答
∵tan(¼π-α)=(1-tanα)/(1+tanα)=-1/3,∴tanα=2,∴sin2α=2tanα/(1+tan²α)=4/5,cos2α=(1-tan²α)/(1+tan²α)=-3/5,∴sin(2α+¼π)=½√2(sin2α+cos2α)=√2/10.