Question

Find the value of $\cot \left(-135°\right)$ along with the steps.

Answer 1

Calculate the value of given expression

Given, $\cot \left(-135°\right)$.

$\cot$ function can be written as the ratio of $\cos$ and $\sin$ function.

$\begin{array}{rcl}\cot \left(-135°\right)& =& \frac{\cos \left(-135°\right)}{\sin \left(-135°\right)}\\ & =& \frac{\cos \left(360-135\right)}{\sin \left(360-135\right)}\\ & =& \frac{\cos \left(225\right)}{\sin \left(225\right)}\\ & =& \frac{\cos \left(180+45\right)}{\sin \left(180+45\right)}\\ & =& \frac{\cos \left(45°\right)}{\sin \left(45°\right)}\\ & =& \frac{{\displaystyle \frac{1}{\sqrt{2}}}}{{\displaystyle \frac{1}{\sqrt{2}}}}\\ & =& 1\end{array}$

Hence, the value of $\cot \left(-135°\right)=1$.