If A is an angle such that sec(A) + tan(A) = 2, evaluate cos(A)

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）

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

cos(A)=4/5