A) \[x+y\ne 0\]
B) \[x=y,\,\,x\ne 0,\,\,y\ne 0\]
C) \[x=y\]
D) \[x\ne 0,\,\,y\ne 0\]
Correct Answer: B
Solution :
Key Idea: \[{{\sin }^{2}}\theta \]is lies between \[0\] to\[1\]. We know that\[{{\sin }^{2}}\theta \ge 1\] \[\Rightarrow \] \[\frac{4xy}{{{(x+y)}^{2}}}\ge 1\] \[\Rightarrow \] \[4xy\ge {{(x+y)}^{2}}\] \[\Rightarrow \] \[{{(x-y)}^{2}}\le 0\] \[\Rightarrow \] \[x-y=0\] \[\Rightarrow \] \[y=x\] and \[x\ne 0,\,\,y\ne 0\]
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