[tex]a^2=8^2-6^2\\\\a^2=64-36\\\\a^2=28\\\\a=2\sqrt7\\\\\tan\alpha+\tan\beta=\frac{6}{2\sqrt7}+\frac{2\sqrt7}{6}=\frac{36}{12\sqrt7}+\frac{(2\sqrt7)^2}{12\sqrt7}=\\\\=\frac{36+(\sqrt{28})^2}{12\sqrt7}=\frac{36+28}{12\sqrt7}=\frac{64}{12\sqrt7}=\frac{64\sqrt7}{12\cdot7}=\frac{64\sqrt7}{84}=\frac{16\sqrt7}{21}[/tex]
