Question

sin(π/4 -α)=5/13,且α∈（0,π/2）,则cos2α / cos(π/4 +α）=?

Answer 1

由于α∈（0,π/2）,所以(π/4 -α)∈(-π/4,π/4)

又sin(π/4 -α)=5/13,故cos^2(π/4 -α)=1-sin^2(π/4 -α)=1-(5/13)^2=144/169,

即cos(π/4 -α)=12/13

所以sin2(π/4 -α)=2sin(π/4 -α)cos(π/4 -α)=2*(5/13)*(12/13)=120/169,

即sin(π/2 -2α)=cos2α=120/169

cos(π/4 +α)=cos[π/2- (π/4 -α)]=sin(π/4-α)=5/13

因此cos2α / cos(π/4 +α)=(120/169)/(5/13)=24/13