Cot  Tan Formula
The six trigonometric ratios are the ratios of the sides of a rightangled triangle. The Tanθ is the ratio of the altitude, base of the right triangle, and Cotθ is the ratio of the base, altitude of the right triangle. The cot  tan formula presents an inverse relationship between Cotθ and Tanθ.
What is the relationship between Cotθ and Tanθ ?
In this cot  tan formula the two trigonometric ratios of Cotangent and Tangent are inversely related. Tanθ is the ratio altitude and base of a right triangle, and Cotθ is the ratio of the base and altitude of a right triangle.
Cotθ = 1/Tanθ
Let us try out a few examples to better understand the CotTan Formula.
Solved Examples on Cot  Tan Formula

Example 1: The value of \(Tan \theta = \frac{4}{7} \). Find the value of \(Cot \theta \).
Solution:
Given \(Tan \theta = \frac{4}{7} \).
\(\begin{align} Cot\theta &= \dfrac{1}{Tan\theta} \\ &=\dfrac{1}{\frac{4}{7}} \\&= \frac{7}{4} \end{align}\)
Answer: Hence \(Cot \theta = \frac{7}{4} \) 
Example 2: The altitude of a right triangle is 9 units and the base of the triangle is 13 units. Find the values of \(Tan \theta \) and \(Cot \theta \).
Solution:
The given Altitude = 9 units and Base = 13 units.
\(Tan \theta = \frac{Altitude}{Base} = \frac{9}{13} \)
\(Cot \theta = \frac{Base}{Altitude} = \frac{13}{9} \)
Answer: Tanθ = 9/13, Cotθ = 13/9