question_answer

If \[m\cos \theta +n\,\sin \theta =r,\] then find the value of\[{{(m\,\,\sin \theta -n\,\,\cos \theta )}^{2}}\].

A)  \[{{m}^{2}}+{{n}^{2}}-{{r}^{2}}\]          

B)  \[{{r}^{2}}+{{m}^{2}}-{{n}^{2}}\]

C)  \[{{n}^{2}}+{{r}^{2}}-{{m}^{2}}\]                      

D)  \[-\,{{m}^{2}}+{{r}^{2}}-{{n}^{2}}\]

E)  None of these