If A is an angle such that sec(A) + tan(A) = 2,evaluate cos(A)求 COA A.求 COS..A 请写具体

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IfAisananglesuchthatsec(A)+tan(A)=2,evaluatecos(A)求COAA.求COS..A请写具体IfAisananglesuchthatsec(A)+tan(A)

If A is an angle such that sec(A) + tan(A) = 2,evaluate cos(A)求 COA A.求 COS..A 请写具体
If A is an angle such that sec(A) + tan(A) = 2,evaluate cos(A)
求 COA A.
求 COS..A 请写具体

If A is an angle such that sec(A) + tan(A) = 2,evaluate cos(A)求 COA A.求 COS..A 请写具体
sec(A)=1/cos(A),tan(A)=sin(A)/cos(A)
sec(A) + tan(A)=1/cos(A)+sin(A)/cos(A)=(1+sin(A))/cos(A)=2
1+sin(A)=2cos(A) sin(A)=2cos(A)-1
sin^2(A)+cos^2(A)=1
(2cos(A)-1)^2+cos^2(A)=1
cos(A)=4/5(因为存在secA,0舍去)

cos(A)=4/5

secA=1/cosA tanA=sinA/cosA (1+sinA)/cosA=2 与 sinA^2+cosA^2=1联立解出sinA cosA就Ok啦! 记得舍掉0,因为secA=1/cosA中cosA不能为0

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