\(\frac{sina}{cosa}+\frac{cosa}{sina}=3\Leftrightarrow\frac{sin^2a+cos^2a}{sina.cosa}=3\Rightarrow sina.cosa=\frac{1}{3}\)
\(A^2=\left(sina+cosa\right)^2=sin^2a+cos^2a+2sina.cosa\)
\(\Rightarrow A^2=1+2.\frac{1}{3}=\frac{4}{3}\)
\(\Rightarrow A=\pm\frac{2\sqrt{3}}{3}\)
(Nếu trong tam giác vuông thì \(A=\frac{2\sqrt{3}}{3}\))