question_answer

If \[\operatorname{cosec}\theta -\sin \theta =m\] and \[\sec \theta -\cos \theta =n\], then

A)  \[{{({{m}^{2}}n)}^{\frac{2}{3}}}+{{(m{{n}^{2}})}^{\frac{2}{3}}}=1\]

B)  \[{{({{m}^{2}}{{n}^{2}})}^{\frac{1}{3}}}+{{(m{{n}^{2}})}^{\frac{1}{3}}}=1\]

C)  \[{{(m{{n}^{2}})}^{\frac{1}{3}}}+{{({{m}^{2}}{{n}^{2}})}^{\frac{2}{3}}}=1\]

D)  \[{{({{m}^{2}}{{n}^{2}})}^{\frac{1}{3}}}+{{({{m}^{2}}{{n}^{2}})}^{\frac{1}{3}}}=1\]

E)  None of these