Question

If $cosec\theta -cot\theta =p$, then $cosec\theta +cot\theta =$

• A. 1/p
• B. -1/p
• C. -p
• D. $p^2$

Answer 1

The correct option is A 1/p

$\csc \theta -\cot \theta =p$

$\Rightarrow (\csc \theta -\cot \theta )(\csc \theta +\cot \theta )=p(\csc \theta +\cot \theta )$

$\Rightarrow {\csc }^2\theta -{\cot }^2\theta =p(\csc \theta +\cot \theta )$

$\Rightarrow 1=p(\csc \theta +\cot \theta )$

$\therefore \csc \theta +\cot \theta =\frac{1}{p}$