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