Respuesta :

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].

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