Question

If $f\left(\theta \right)=cot\theta =-2$find$f\left(\theta +\pi \right)$.

Short answer

The value of $f\left(\theta +\pi \right)$is$\frac{1}{2}$.

Step-by-step solution

Step 1. Given information.

Consider the given information$f\left(\theta \right)=cot\theta$and the value of$cot\theta =-2$.

Step 2. Formula used.

$cot\left(A+B\right)=\frac{cotAcotB-1}{cotA+cotB}$

Step 3. Finding the value of fθ+π.

Substitute the value in formula.

$$\begin{gathered} cot\left(A+B\right)=\frac{cotAcotB-1}{cotA+cotB} \\ cot\left(A+B\right)=\frac{1}{2} \end{gathered}$$

Therefore the value of$f\left(\theta +\pi \right)$is$\frac{1}{2}$.