Find the value of

To find: Value of $\cot \frac{13 \pi}{4}$

We have

$\cot \frac{13 \pi}{4}$

Putting $\pi=180^{\circ}$

$=\cot \left(\frac{13 \times 180^{\circ}}{4}\right)$

$=\cot \left(13 \times 45^{\circ}\right)$

$=\cot \left(585^{\circ}\right)$

$=\cot \left[90^{\circ} \times 6+45^{\circ}\right]$

$=\cot 45^{\circ}$

[Clearly, $585^{\circ}$ is in IIIrd Quadrant and the multiple of $90^{\circ}$ is even]

$=1\left[\because \cot 45^{\circ}=1\right]$