Question

sin(π/4+α)=5/13 α∈（π/4,3π/4） 求(1+tanα)/(1-tanα)

Answer 1

因为 α ∈(π/4,3π/4),

所以 π/4 +α ∈(π/2,π),

又因为 sin (π/4 +α) =5/13,

所以 cos (π/4 +α) = -根号[ 1 -(5/13)^2 ]

= -12/13.

所以 tan (π/4 +α) =sin (π/4 +α) /cos (π/4 +α)

= -5/12.

又因为 tan (π/4 +α) =(tan π/4 +tan α) /(1 -tan π/4 tan α)

=(1 +tan α) /(1 -tan α),

所以 (1 +tan α) /(1 -tan α) = -5/12.

= = = = = = = = =

以上计算可能有误.

注意 tan π/4 =1,因此

(1 +tan α) /(1 -tan α) =tan (π/4 +α).