Question

If $\text{cosec}\theta -\cot \theta =q,$ then the value of $\text{cosec}\theta$ is

• A. $q+\frac{1}{q}$
• B. $q-\frac{1}{q}$
• C. $\frac{1}{2}(q+\frac{1}{q})$
• D. none of these

Answer 1

The correct option is C $\frac{1}{2}(q+\frac{1}{q})$

Let $\csc \theta -\cot \theta =q$ ...(1)
$\frac{(\csc \theta -\cot \theta )(\csc \theta +\cot \theta )}{\csc \theta +\cot \theta }=q\Rightarrow \frac{{\csc }^2\theta -{\cot }^2\theta }{\csc \theta +\cot \theta }=q$
$\Rightarrow \csc \theta +\cot \theta =\frac{1}{q}$ ...(2)
Adding (1) & (2) we get,
$2\csc \theta =q+\frac{1}{q}\therefore \csc \theta =\frac{1}{2}(q+\frac{1}{q})$
Ans: C