A) 2
B) 0
C) 3
D) 4
E) 1
Correct Answer: E
Solution :
Given that, \[x{{\sin }^{3}}\theta +y{{\cos }^{3}}\theta =\sin \theta \cos \theta \] ?.(i) and \[x\sin \theta =y\cos \theta \] .. .(ii) On using Eqs. (i) and (ii), we get \[y\text{ }\cos \theta \text{ }{{\sin }^{2}}\theta +y\text{ }{{\cos }^{3}}\theta =\sin \theta \text{ }\cos \theta \] \[\Rightarrow \] \[y\text{ }cos\theta (si{{n}^{2}}\theta +co{{s}^{2}}\theta )=sin\theta \text{ }cos\theta \] \[\Rightarrow \] \[y=sin\text{ }\theta \] On putting the value of y in Eq (ii), we get \[x\text{ }sin\theta =sin\theta \text{ }cos\theta \] \[\Rightarrow \] \[x=cos\theta \]
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