If p=cosec θ- θ and q=(cosec θ+ θ)^ -1 , then which one of the...

$\mathrm{p}=\operatorname{cosec} \theta-\cot \theta$$\begin{aligned} & \mathrm{q}=(\operatorname{cosec} \theta+\cot \theta)^{-1} \\ & \Rightarrow \frac{1}{q}=\operatorname{cosec} \theta+\cot \theta\end{aligned}$We know, $\operatorname{cosec}^2 \theta-\cot ^2 \theta=1\begin{aligned} & \Rightarrow(\operatorname{cosec} \theta+\cot \theta)(\operatorname{cosec} \theta-\cot \theta)=1 \\ & \Rightarrow\left(\frac{1}{q}\right)(p)=1 \\ & \Rightarrow \mathrm{p}=\mathrm{q}\end{aligned}$$$