sin(π/4 -α)=5/13,且α∈（0,π/2）,则cos2α / cos(π/4 +α）=?
问题描述：
sin(π/4 -α)=5/13,且α∈（0,π/2）,则cos2α / cos(π/4 +α）=?
sin(π/4 -α)=5/13,且α∈（0,π/2）,则cos2α / cos(π/4 +α）=?
答
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)*...你看错题了 是 cos(π/4 +α）π/2- (π/4 -α)=π/4 +α利用诱导公式sin(π/2-α)=cosα