Cotangent and tangent are reciprocals, as they should be. However, you cannot have this value of cosine for the same angle. Since $\displaystyle{\tan{{X}}}=\frac{{5}}{{1}}\usepackage{cmbright}\Huge\$ , you could have $\displaystyle{o}={5}\usepackage{cmbright}\Huge\$ and $\displaystyle{a}={1}\usepackage{cmbright}\Huge\$ . If $\displaystyle{\cos{{X}}}=\frac{{1}}{{6}}=\frac{{a}}{{h}}\usepackage{cmbright}\Huge\$ , then $\displaystyle{h}={6}\usepackage{cmbright}\Huge\$ . But the lengths 1, 5, and 6 do not satisfy the Pythagorean Theorem.