Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

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

$\Rightarrow (cosec\theta -\cot \theta )=\frac{cose{c}^2\theta -{\cot }^2\theta }{3}$

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

$\Rightarrow (cosec\theta +\cot \theta )=3$

Hence, the answer is $3.$