Question

Cot theta - cosec theta = P , then cot theta + cosec theta =​

Answer 1

Recall $\csc^2\theta=\cot^2\theta+1$

or, $\csc^2\theta-\cot^2\theta=1 \implies (\csc\theta+\cot\theta)(\csc\theta-\cot\theta)=1$

Now, $\cot \theta - \csc \theta = P$

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

or $(\csc\theta+\cot\theta)=-\frac{1}{P}$