Q.92 - Precalculus Enhanced with Graphing Utilities

Question

if $\cot \left(\theta \right)=-2$ find $\cot \left(\theta \right)+\cot \left(\theta -\pi \right)+\cot \left(\theta -2\pi \right)$

Step-by-Step Solution

Answer

The value of $\cot \left(\theta \right)+\cot \left(\theta -\pi \right)+\cot \left(\theta -2\pi \right) is -6$

Step 1: Given information

We are given $\cot \left(\theta \right)=-2$

Step 2: Use periodicity property of trigonometric function cot θ + π = cot θ

We get,

$$\begin{gathered} \cot \left(\theta \right)+\cot \left(\theta -\pi \right)+\cot \left(\theta -2\pi \right) \\ \cot \left(\theta \right)+\cot \left(\theta \right)+\cot \left(\theta -\pi \right) \\ \cot \left(\theta \right)+\cot \left(\theta \right)+\cot \left(\theta \right) \\ 3\cot \left(\theta \right) \\ =3(-2) \\ =-6 \end{gathered}$$

Step 3: Conclusion

The value of $\cot \left(\theta \right)+\cot \left(\theta -\pi \right)+\cot \left(\theta -2\pi \right) is -6$