Question

If $\csc \theta -\cot \theta =6$ then $\csc \theta +\cot \theta$

Answer 1

$\csc \theta -\cot \theta =6$

We know ${\csc }^2\theta -{\cot }^2\theta =1$

$(\csc \theta -\cot \theta )$$(\csc \theta +\cot \theta )=1$

$\Rightarrow \left(6\right)$$(\csc \theta +\cot \theta )=1$

$\therefore \csc \theta +\cot \theta =\frac{1}{6}$