question_answer

If \[\operatorname{cosec}\theta -\sin \theta =\frac{1}{p}\] and \[\sec \theta -\cos \theta =\frac{1}{q}\], then _______.

A)  \[{{({{p}^{2}}q)}^{\frac{2}{3}}}+{{(p{{q}^{2}})}^{\frac{2}{3}}}=1\]    

B)  \[{{({{p}^{2}}q)}^{\frac{1}{3}}}+{{(p{{q}^{2}})}^{\frac{1}{3}}}=1\]

C)  \[{{\left( \frac{1}{{{p}^{2}}q} \right)}^{\frac{2}{3}}}+{{\left( \frac{1}{p{{q}^{2}}} \right)}^{\frac{2}{3}}}=1\]

D)  \[{{\left( \frac{1}{{{p}^{2}}q} \right)}^{\frac{1}{3}}}+{{\left( \frac{1}{p{{q}^{2}}} \right)}^{\frac{1}{3}}}=1\]

E)  None of these