Question:
Find the value of
$\cot \left(585^{\circ}\right)$
Solution:
To find: Value of $\cot \frac{13 \pi}{4}$
We have
$\cot \left(585^{\circ}\right)=\cot \left[90^{\circ} \times 6+45^{\circ}\right]$
$=\cot 45^{\circ}$
[Clearly, $585^{\circ}$ is in III $^{\text {rd }}$ Quadrant and the multiple of $90^{\circ}$ is even]
$=1\left[\because \cot 45^{\circ}=1\right]$
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