1 Answer

Leslieann · Answer 1 · 2022-06-07T15:11:36+0000

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
.

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