Question

If $\text{cosec}\theta -\cot \theta =x$ then $\text{cosec}\theta +\cot \theta =$ _____

• A. $x$
• B. $2x$
• C. $\frac{1}{x}$
• D. $\frac{1}{2x}$

Answer 1

Answer: (C)

$\frac{1}{x}$

$cosec\theta -\cot \theta =x$

Now, $cose{c}^2\theta -{\cot }^2\theta =1$

$\Rightarrow (cosec\theta -\cot \theta )(cosec\theta +\cot \theta )=1$

$\Rightarrow x(cosec\theta +\cot \theta )=1$

$\Rightarrow cosec\theta +\cot \theta =\frac{1}{x}$

Hence, the answer is $\frac{1}{x}.$