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If $0 < x, y < 2 π$ , the number of solutions of the system of equations $\sin x \sin y = 3 / 4$ and $\cos x \cos y = 1 / 4$ is

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Correct option is C

cos⁡(x−y)=1 ⇒ x−y=0 (Note Note x−y≠2π)⇒ x=ycos⁡(x+y)=−1/2⇒x+y=120∘ or240∘⇒x=y=60∘or x=y=120∘

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If 0<x,y<2π , the number of solutions of the system of equations sin⁡x sin⁡y=3/4 and cos⁡x cos⁡y=1/4 is

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If $0 < x, y < 2 π$ , the number of solutions of the system of equations $\sin x \sin y = 3 / 4$ and $\cos x \cos y = 1 / 4$ is