If tan A=34 and A+B=90°, then what is the value of cot B?

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 $\frac{3}{4}$