$\begin{array}{l} \tan a = 2 \Rightarrow {\tan ^2}a = 4\\ + {\tan ^2}a + 1 = \dfrac{1}{{{{\cos }^2}a}} \Rightarrow 5 = \dfrac{1}{{{{\cos }^2}a}} \Rightarrow {\cos ^2}a = \dfrac{1}{5}\\ C = 5{\cos ^2}a + 2{\sin ^2}a = 2{\cos ^2}a + 2{\sin ^2}a + 3{\cos ^2}a\\ C = 2 + 3{\cos ^2}a = 2 + 3.\dfrac{1}{5} = 2 + \dfrac{3}{5} = \dfrac{{13}}{5} \end{array}$