Question:
If $\tan A=\frac{3}{4}$ and $A+B=90^{\circ}$, then what is the value of $\cot \mathrm{B} ?$
Solution:
Given that:
$A+B=90^{\circ}$
$\tan A=\frac{3}{4}$
$A+B=90^{\circ}$
$\Rightarrow B=90^{\circ}-A$
$\Rightarrow \cot B=\cot \left(90^{\circ}-A\right)$
$\Rightarrow \cot B=\tan A$
$\Rightarrow \cot B=\frac{3}{4}\left[\cot \left(90^{\circ}-A\right)=\tan A\right]$
Hence the value of $\cot B$ is $\frac{3}{4}$