Question

If $\text{cosec}\theta -\cot \theta =\frac{1}{3}$, then the value of $(\text{cosec}\theta +\cot \theta )$ is :

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

Given:

$\text{cosec}\theta -\cot \theta =\frac{1}{3}$

$\Rightarrow 3(\text{cosec}\theta -\cot \theta )=({\text{cosec}}^2\theta -\cot {}^2\theta )$

[Since, $1={\text{cosec}}^2\theta -\cot {}^2\theta$]

$\Rightarrow 3(\text{cosec}\theta -\cot \theta )=(\text{cosec}\theta -\cot \theta )(\text{cosec}\theta +\cot \theta )$

$\Rightarrow (\text{cosec}\theta +\cot \theta )=3$

$\therefore$ required answer is $3.$

Hence, Option D is correct.