Question

已知fx=tan(3x+π/4)

Answer 1

1.f(π/9)=tan(π/3+π/4)

=(tanπ/3+tanπ/4)/(1-tanπ/3tanπ/4)

=(√3+1)/(1-√3)

=-√3-2

2.

∵f(a/3+π/4)=2

∴tan(a+3π/4+π/4)

= tan(π+a)=tana=2

sina/cosa=2

sina=2cosa代入sin²a+cos²a=1

cos²a=1/5

∴cos(a-Pai/4)=根号2/2*(cosa+sina)=根号2/2*(-根号5/5-2根号5/5)=-3根号10/10