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）=?

来源：学生作业帮助网编辑：作业帮时间：2024/05/07 13:05:02

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）=?
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

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WASHINGTON (Cai Xiuli) October 30, the eighth in Wuhan, China Wuhan International Racing Festival on the National Championship race speed, Heilongjiang Equestrian Team rider Aobai Yun-year-old group were driving the Saab 2100 m title. In the speed race competition, a total of more than 200 horses from around the country to participate in six levels of competition. The first day, in addition to an indefinite group of 1800 m horse projects, Heilongjiang equestrian team of five horses all the items into the final. Which, by the rider to control the Saab Ao Baiyun face strong opponents to score 2 minutes 22 seconds led the way won the title. This year is the province since the establishment of the equestrian team get the first title, but also Woxing sports reform and innovation process, following the "city of the provincial team to do", "provincial team-run" mode, try to explore taking on individual projects. " provincial team enterprises do "was a success. (Editor: Moon Shadow)
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α∈（0，π/2）,sin(π/4 -α)=5/13, α< π/4, cos(π/4 -α)=12/13
2α< π/2, cos(π/4 -α))*sin(π/4 -α)=0.5sin(π/2 -2α)=1/2cos2α=60/169
cos(π/4 +α）=sin(π/2-(π/4 +α))=sin(π/4 -α)=5/13,
则cos2α / cos(π/4 +α）=24/13

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