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$\sin θ = \frac{1}{2} (\sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}})$ necessarily implies

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Correct option is C

Since -1≤sinx≤1, ⇒-1≤12 xy+yx≤1 ⇒-2xy≤x+y≤2xy⇒x+y≤2xy ⇒x+y-2xy≤0 ⇒x-y2≤0 ⇒x-y2=0 ∵ square in non-negative⇒x=y

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sinθ=12xy+yx necessarily implies

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$\sin θ = \frac{1}{2} (\sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}})$ necessarily implies