\(A=\dfrac{\left(sina+cosa\right)\left(sin^2a-sina\cdot cosa+cos^2a\right)}{cosa\cdot sina\left(2cosa+sina\right)}\)
\(=\dfrac{\left(sina+cosa\right)\left(1-sina\cdot cosa\right)}{cosa\cdot sina\left(2\cdot cosa+sina\right)}\)
\(1+tan^2a=\dfrac{1}{cos^2a}=1+\dfrac{9}{25}=\dfrac{34}{25}\)
\(\Leftrightarrow cosa=\dfrac{5}{\sqrt{34}}\)
=>\(sina=\dfrac{3}{\sqrt{34}}\)
\(=\dfrac{\left(sina+cosa\right)\left(1-sina\cdot cosa\right)}{cosa\cdot sina\left(2\cdot cosa+sina\right)}\)
\(=\dfrac{\left[\left(\dfrac{3}{\sqrt{34}}+\dfrac{5}{\sqrt{34}}\right)\left(1-\dfrac{15}{34}\right)\right]}{\dfrac{15}{34}\cdot\left(\dfrac{10}{\sqrt{34}}+\dfrac{3}{\sqrt{34}}\right)}\)
\(=\dfrac{\dfrac{8}{\sqrt{34}}\cdot\dfrac{19}{34}}{\dfrac{15}{34}\cdot\dfrac{13}{\sqrt{34}}}=\dfrac{8\cdot19}{15\cdot13}=\dfrac{152}{195}\)
