Given:
[tex]\cot \theta = -2[/tex]
To find:
The value of [tex]\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)[/tex].
Solution:
We know that,
[tex]\cot (\theta -n\pi)=\cot \theta[/tex] ...(i)
Where n is an integer.
We have,
[tex]\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)[/tex]
Using (i), it can be written as
[tex]\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=\cot \theta +\cot \theta +\cot \theta [/tex]
[tex]\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=3\cot \theta[/tex]
It is given that [tex]\cot \theta = -2[/tex].
[tex]\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=3(-2)[/tex]
[tex]\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=-6[/tex]
Therefore, the value of the given function expression is [tex]-6[/tex].
