Question

If cosec theta-cot theta is equal to 1/M then what is the value of cosec theta +cot theta ​

Answer 1

Given:

`\text{cosec}\theta -\cot \theta =(1)/(M)`

To find:

The value of
`\text{cosec}\theta +\cot \theta`.

Solution:

We have,

`\text{cosec}\theta -\cot \theta =(1)/(M)`

We know that,

`\text{cosec}^2\theta -\cot^2 \theta=1`

It can be written as:

`(\text{cosec}\theta -\cot \theta)(\text{cosec}\theta +\cot \theta)=1`

`(1)/(M)* (\text{cosec}\theta +\cot \theta)=1`

`\text{cosec}\theta +\cot \theta=1* M`

`\text{cosec}\theta +\cot \theta=M`

Therefore, the value of
`\text{cosec}\theta +\cot \theta` is
`M`.