Question

Consider triangle A B C, where angle C is the right angle. Explain why tan A=cot B in any such triangle.

Answer 1

The diagram of Triangle ABC where C is the right angle is attached below:

$\begin{gathered} \tan A=\frac{Side\text{ opposite of A}}{Side\text{ Adjacent to A}} \\ =\frac{a}{b} \end{gathered}$

Similarly:

$\begin{gathered} \tan B=\frac{Side\text{ opposite of B}}{Side\text{ Adjacent to B}} \\ =\frac{b}{a} \\ \cot B=\frac{1}{\tan B} \\ =\frac{1}{\frac{b}{a}} \\ =\frac{a}{b} \end{gathered}$

We can see therefore that tan A = cot B.