Question

计算:1/(1-tan派/8) - 1/(1+tan派/8)

Answer 1

1/(1-tanx)=1/(1- [sinx/cosx])=cosx/(cosx-sinx) ;1/(1+tanx)=1/(1+ [sinx/cosx])=cosx/(cosx+sinx)

1/(1-tanθ) - 1/(1+tanθ)=cosx*(2sinx /[cosx)^2 - (sinx)^2]=sin2x /cos2x

=>所求 =tanπ/4 =1.....ans