Question

How do I find the angle forTan2B= Cot2B

Answer 1

We have the following:

`\tan 2B=\cot 2B`

resolving for B:

`\begin{gathered} \tan \: 2B-\cot \: 2B=0 \\ (1)/(\cot2B)-\cot 2B=0 \end{gathered}`

For this to be true, both have to be 1 or -1, like this

`\begin{gathered} (1)/(1)-1=0 \\ 1-1=0 \\ or \\ (1)/(-1)-(-1)=0 \\ -1+1=0 \end{gathered}`

Therefore:

`\begin{gathered} \cot 2B=1\rightarrow B=(\pi)/(8)=22.5 \\ \cot 2B=-1\rightarrow B=(3\pi)/(8)=67.5 \end{gathered}`

Therefore, B can be 22.5 ° or 67.5 °