A) \[0\]
B) \[2\]
C) \[4\]
D) \[1\]
Correct Answer: D
Solution :
Given, \[x\,\sin \theta -y\,\cos \,\theta =0\] ?.(i) and \[x\,{{\sin }^{3}}\theta +y{{\cos }^{3}}\theta =\sin \theta \,\cos \theta \] ?.(ii) On multiplying Eq. (i) by \[{{\sin }^{2}}\theta \] and subtracting from Eq. (ii), we get \[y\,{{\cos }^{3}}\theta +y\cos \,{{\sin }^{2}}\theta =\sin \theta \,\cos \theta \] \[\Rightarrow \] \[y\,\cos \theta (1)=sin\theta \,cos\theta \] \[\Rightarrow \] \[y=\sin \theta \] From Eq. (i), \[x\,\sin \theta =\sin \theta \,\cos \theta \] \[\Rightarrow \] \[x=\cos \theta \] Now, \[{{x}^{2}}+{{y}^{2}}={{\cos }^{2}}\theta +{{\sin }^{2}}\theta =1\]
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