Question

If cot theta = -2, find the value of cot theta + cot (theta -pi) + cot (theta-2pi)

Answer 1

Given:

$\cot \theta = -2$

To find:

The value of $\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)$.

Solution:

We know that,

$\cot (\theta -n\pi)=\cot \theta$         ...(i)

Where n is an integer.

We have,

$\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)$

Using (i), it can be written as

$\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=\cot \theta +\cot \theta +\cot \theta$

$\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=3\cot \theta$

It is given that $\cot \theta = -2$.

$\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=3(-2)$

$\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=-6$

Therefore, the value of the given function expression is $-6$.