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}} \\ =(a)/(b) \end{gathered}`

Similarly:

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

We can see therefore that tan A = cot B.